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Update examples in planstats.sgml for 8.3, and improve some aspects of

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that discussion.  Add a link from perform.sgml.
REL8_3_STABLE
Tom Lane 18 years ago
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  1. 36
      doc/src/sgml/perform.sgml
  2. 454
      doc/src/sgml/planstats.sgml

36
doc/src/sgml/perform.sgml
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@ -1,4 +1,4 @@
<!-- $PostgreSQL: pgsql/doc/src/sgml/perform.sgml,v 1.67 2007/11/28 15:42:31 petere Exp $ -->
<!-- $PostgreSQL: pgsql/doc/src/sgml/perform.sgml,v 1.68 2007/12/28 21:03:31 tgl Exp $ -->
<chapter id="performance-tips">
<title>Performance Tips</title>
@ -8,7 +8,7 @@
</indexterm>
<para>
Query performance can be affected by many things. Some of these can
Query performance can be affected by many things. Some of these can
be manipulated by the user, while others are fundamental to the underlying
design of the system. This chapter provides some hints about understanding
and tuning <productname>PostgreSQL</productname> performance.
@ -138,7 +138,7 @@ EXPLAIN SELECT * FROM tenk1;
Rows output is a little tricky because it is <emphasis>not</emphasis> the
number of rows processed or scanned by the plan node. It is usually less,
reflecting the estimated selectivity of any <literal>WHERE</>-clause
conditions that are being
conditions that are being
applied at the node. Ideally the top-level rows estimate will
approximate the number of rows actually returned, updated, or deleted
by the query.
@ -469,8 +469,8 @@ EXPLAIN ANALYZE SELECT * FROM tenk1 t1, tenk2 t2 WHERE t1.unique1 &lt; 100 AND t
One component of the statistics is the total number of entries in
each table and index, as well as the number of disk blocks occupied
by each table and index. This information is kept in the table
<link linkend="catalog-pg-class"><structname>pg_class</structname></link>, in
the columns <structfield>reltuples</structfield> and
<link linkend="catalog-pg-class"><structname>pg_class</structname></link>,
in the columns <structfield>reltuples</structfield> and
<structfield>relpages</structfield>. We can look at it with
queries similar to this one:
@ -493,7 +493,7 @@ SELECT relname, relkind, reltuples, relpages FROM pg_class WHERE relname LIKE 't
</para>
<para>
For efficiency reasons, <structfield>reltuples</structfield>
For efficiency reasons, <structfield>reltuples</structfield>
and <structfield>relpages</structfield> are not updated on-the-fly,
and so they usually contain somewhat out-of-date values.
They are updated by <command>VACUUM</>, <command>ANALYZE</>, and a
@ -517,7 +517,8 @@ SELECT relname, relkind, reltuples, relpages FROM pg_class WHERE relname LIKE 't
<firstterm>selectivity</> of <literal>WHERE</> clauses, that is,
the fraction of rows that match each condition in the
<literal>WHERE</> clause. The information used for this task is
stored in the <link linkend="catalog-pg-statistic"><structname>pg_statistic</structname></link>
stored in the
<link linkend="catalog-pg-statistic"><structname>pg_statistic</structname></link>
system catalog. Entries in <structname>pg_statistic</structname>
are updated by the <command>ANALYZE</> and <command>VACUUM
ANALYZE</> commands, and are always approximate even when freshly
@ -530,7 +531,8 @@ SELECT relname, relkind, reltuples, relpages FROM pg_class WHERE relname LIKE 't
<para>
Rather than look at <structname>pg_statistic</structname> directly,
it's better to look at its view <structname>pg_stats</structname>
it's better to look at its view
<link linkend="view-pg-stats"><structname>pg_stats</structname></link>
when examining the statistics manually. <structname>pg_stats</structname>
is designed to be more easily readable. Furthermore,
<structname>pg_stats</structname> is readable by all, whereas
@ -553,13 +555,8 @@ SELECT attname, n_distinct, most_common_vals FROM pg_stats WHERE tablename = 'ro
</para>
<para>
<structname>pg_stats</structname> is described in detail in
<xref linkend="view-pg-stats">.
</para>
<para>
The amount of information stored in <structname>pg_statistic</structname>,
in particular the maximum number of entries in the
The amount of information stored in <structname>pg_statistic</structname>
by <command>ANALYZE</>, in particular the maximum number of entries in the
<structfield>most_common_vals</> and <structfield>histogram_bounds</>
arrays for each column, can be set on a
column-by-column basis using the <command>ALTER TABLE SET STATISTICS</>
@ -570,7 +567,12 @@ SELECT attname, n_distinct, most_common_vals FROM pg_stats WHERE tablename = 'ro
columns with irregular data distributions, at the price of consuming
more space in <structname>pg_statistic</structname> and slightly more
time to compute the estimates. Conversely, a lower limit might be
appropriate for columns with simple data distributions.
sufficient for columns with simple data distributions.
</para>
<para>
Further details about the planner's use of statistics can be found in
<xref linkend="planner-stats-details">.
</para>
</sect1>
@ -913,7 +915,7 @@ SELECT * FROM x, y, a, b, c WHERE something AND somethingelse;
are designed not to write WAL at all if <varname>archive_mode</varname>
is off. (They can guarantee crash safety more cheaply by doing an
<function>fsync</> at the end than by writing WAL.)
This applies to the following commands:
This applies to the following commands:
<itemizedlist>
<listitem>
<para>

454
doc/src/sgml/planstats.sgml
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@ -1,27 +1,22 @@
<!-- $PostgreSQL: pgsql/doc/src/sgml/planstats.sgml,v 1.8 2007/01/31 20:56:18 momjian Exp $ -->
<!-- $PostgreSQL: pgsql/doc/src/sgml/planstats.sgml,v 1.9 2007/12/28 21:03:31 tgl Exp $ -->
<chapter id="planner-stats-details">
<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,
This chapter builds on the material covered in <xref
linkend="using-explain"> and <xref linkend="planner-stats"> to show some
additional details about how the planner uses the
system statistics to estimate the number of rows each part of a query might
return. This is a significant part of the planning process,
providing much of the raw material for cost calculation.
</para>
<para>
The intent of this chapter is not to document the code &mdash;
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 behavior of earlier (or later) versions might vary.
The intent of this chapter is not to document the code in detail,
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.
</para>
<sect1 id="row-estimation-examples">
@ -33,160 +28,163 @@
</indexterm>
<para>
Using examples drawn from the regression test database, let's start with a
very simple query:
The examples shown below use tables in the <productname>PostgreSQL</>
regression test database.
The outputs shown are taken from version 8.3.
The behavior of earlier (or later) versions might vary.
Note also that since <command>ANALYZE</> uses random sampling
while producing statistics, the results will change slightly after
any new <command>ANALYZE</>.
</para>
<para>
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)
Seq Scan on tenk1 (cost=0.00..458.00 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>:
How the planner determines the cardinality of <structname>tenk1</structname>
is covered in <xref linkend="planner-stats">, but is repeated here for
completeness. The number of pages and rows is looked up in
<structname>pg_class</structname>:
<programlisting>
SELECT reltuples, relpages FROM pg_class WHERE relname = 'tenk1';
SELECT relpages, reltuples 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 might scale
<structfield>reltuples</structfield> to obtain a row estimate. In this
case it does not, thus:
<programlisting>
rows = 10000
358 | 10000
</programlisting>
These numbers are current as of the last <command>VACUUM</> or
<command>ANALYZE</> on the table. The planner then fetches the
actual current number of pages in the table (this is a cheap operation,
not requiring a table scan). If that is different from
<structfield>relpages</structfield> then
<structfield>reltuples</structfield> is scaled accordingly to
arrive at a current number-of-rows estimate. In this case the values
are correct so the rows estimate is the same as
<structfield>reltuples</structfield>.
</para>
<para>
let's move on to an example with a range condition in its
Let's move on to an example with a range condition in its
<literal>WHERE</literal> clause:
<programlisting>
EXPLAIN SELECT * FROM tenk1 WHERE unique1 &lt; 1000;
QUERY PLAN
------------------------------------------------------------
Seq Scan on tenk1 (cost=0.00..470.00 rows=1031 width=244)
Filter: (unique1 &lt; 1000)
</programlisting>
The planner examines the <literal>WHERE</literal> clause condition:
<programlisting>
unique1 &lt; 1000
QUERY PLAN
--------------------------------------------------------------------------------
Bitmap Heap Scan on tenk1 (cost=24.06..394.64 rows=1007 width=244)
Recheck Cond: (unique1 &lt; 1000)
-&gt; Bitmap Index Scan on tenk1_unique1 (cost=0.00..23.80 rows=1007 width=0)
Index Cond: (unique1 &lt; 1000)
</programlisting>
and looks up the restriction function for the operator
<literal>&lt;</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>
The planner examines the <literal>WHERE</literal> clause condition
and looks up the selectivity function for the operator
<literal>&lt;</literal> in <structname>pg_operator</structname>.
This is held in the column <structfield>oprrest</structfield>,
and the entry in this case is <function>scalarltsel</function>.
The <function>scalarltsel</function> function retrieves the histogram for
<structfield>unique1</structfield> from
<structname>pg_statistics</structname>. For manual queries it is more
convenient to look in the simpler <structname>pg_stats</structname>
view:
<programlisting>
SELECT histogram_bounds FROM pg_stats
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}
{0,993,1997,3050,4040,5036,5957,7057,8029,9016,9995}
</programlisting>
Next the fraction of the histogram occupied by <quote>&lt; 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:
Next the fraction of the histogram occupied by <quote>&lt; 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 bucket (993-1997). 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
selectivity = (1 + (1000 - bucket[2].min)/(bucket[2].max - bucket[2].min))/num_buckets
= (1 + (1000 - 993)/(1997 - 993))/10
= 0.100697
</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>:
the product of the selectivity and the cardinality of
<structname>tenk1</structname>:
<programlisting>
rows = rel_cardinality * selectivity
= 10000 * 0.1031
= 1031
= 10000 * 0.100697
= 1007 (rounding off)
</programlisting>
</para>
<para>
Next let's consider an example with equality condition in its
Next let's consider an example with an equality condition in its
<literal>WHERE</literal> clause:
<programlisting>
EXPLAIN SELECT * FROM tenk1 WHERE stringu1 = 'ATAAAA';
EXPLAIN SELECT * FROM tenk1 WHERE stringu1 = 'CRAAAA';
QUERY PLAN
----------------------------------------------------------
Seq Scan on tenk1 (cost=0.00..470.00 rows=31 width=244)
Filter: (stringu1 = 'ATAAAA'::name)
Seq Scan on tenk1 (cost=0.00..483.00 rows=30 width=244)
Filter: (stringu1 = 'CRAAAA'::name)
</programlisting>
Again the planner examines the <literal>WHERE</literal> clause condition:
Again the planner examines the <literal>WHERE</literal> clause condition
and looks up the selectivity function for <literal>=</literal>, which is
<function>eqsel</function>. For equality estimation the histogram is
not useful; instead the list of <firstterm>most
common values</> (<acronym>MCV</acronym>s) is used to determine the
selectivity. Let's have a look at the MCVs, with some additional columns
that will be useful later:
<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 &mdash; <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
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}
n_distinct | 676
most_common_vals | {EJAAAA,BBAAAA,CRAAAA,FCAAAA,FEAAAA,GSAAAA,JOAAAA,MCAAAA,NAAAAA,WGAAAA}
most_common_freqs | {0.00333333,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003}
</programlisting>
The selectivity is merely the most common frequency (<acronym>MCF</acronym>)
corresponding to the third <acronym>MCV</acronym> &mdash; 'ATAAAA':
Since <literal>CRAAAA</> appears in the list of MCVs, the selectivity is
merely the corresponding entry in the list of most common frequencies
(<acronym>MCF</acronym>s):
<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:
As before, the estimated number of rows is just the product of this with the
cardinality of <structname>tenk1</structname>:
<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
Now consider the same query, but with a constant that is not in the
<acronym>MCV</acronym> list:
<programlisting>
@ -194,116 +192,197 @@ EXPLAIN SELECT * FROM tenk1 WHERE stringu1 = 'xxx';
QUERY PLAN
----------------------------------------------------------
Seq Scan on tenk1 (cost=0.00..470.00 rows=15 width=244)
Seq Scan on tenk1 (cost=0.00..483.00 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,
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
= (1 - (0.00333333 + 0.003 + 0.003 + 0.003 + 0.003 + 0.003 +
0.003 + 0.003 + 0.003 + 0.003))/(676 - 10)
= 0.0014559
</programlisting>
That is, add up all the frequencies for the <acronym>MCV</acronym>s and
subtract them from one &mdash; 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:
That is, add up all the frequencies for the <acronym>MCV</acronym>s and
subtract them from one, then
divide by the number of <emphasis>other</emphasis> distinct values.
This amounts to assuming that the fraction of the column that is not any
of the MCVs is evenly distributed among all the other distinct values.
Notice that there are no null values so we don't have to worry about those
(otherwise we'd subtract the null fraction from the numerator as well).
The estimated number of rows is then calculated as usual:
<programlisting>
rows = 10000 * 0.001465
= 15
rows = 10000 * 0.0014559
= 15 (rounding off)
</programlisting>
</para>
<para>
Let's increase the complexity to consider a case with more than one
condition in the <literal>WHERE</literal> clause:
The previous example with <literal>unique1 &lt; 1000</> was an
oversimplification of what <function>scalarltsel</function> really does;
now that we have seen an example of the use of MCVs, we can fill in some
more detail. The example was correct as far as it went, because since
<structfield>unique1</> is a unique column it has no MCVs (obviously, no
value is any more common than any other value). For a non-unique
column, there will normally be both a histogram and an MCV list, and
<emphasis>the histogram does not include the portion of the column
population represented by the MCVs</>. We do things this way because
it allows more precise estimation. In this situation
<function>scalarltsel</function> directly applies the condition (e.g.,
<quote>&lt; 1000</>) to each value of the MCV list, and adds up the
frequencies of the MCVs for which the condition is true. This gives
an exact estimate of the selectivity within the portion of the table
that is MCVs. The histogram is then used in the same way as above
to estimate the selectivity in the portion of the table that is not
MCVs, and then the two numbers are combined to estimate the overall
selectivity. For example, consider
<programlisting>
EXPLAIN SELECT * FROM tenk1 WHERE unique1 &lt; 1000 AND stringu1 = 'xxx';
EXPLAIN SELECT * FROM tenk1 WHERE stringu1 &lt; 'IAAAAA';
QUERY PLAN
-----------------------------------------------------------
Seq Scan on tenk1 (cost=0.00..495.00 rows=2 width=244)
Filter: ((unique1 &lt; 1000) AND (stringu1 = 'xxx'::name))
QUERY PLAN
------------------------------------------------------------
Seq Scan on tenk1 (cost=0.00..483.00 rows=3077 width=244)
Filter: (stringu1 &lt; 'IAAAAA'::name)
</programlisting>
An assumption of independence is made and the selectivities of the
individual restrictions are multiplied together:
We already saw the MCV information for <structfield>stringu1</>,
and here is its histogram:
<programlisting>
selectivity = selectivity(unique1 &lt; 1000) * selectivity(stringu1 = 'xxx')
= 0.1031 * 0.001465
= 0.00015104
SELECT histogram_bounds FROM pg_stats
WHERE tablename='tenk1' AND attname='stringu1';
histogram_bounds
--------------------------------------------------------------------------------
{AAAAAA,CQAAAA,FRAAAA,IBAAAA,KRAAAA,NFAAAA,PSAAAA,SGAAAA,VAAAAA,XLAAAA,ZZAAAA}
</programlisting>
The row estimates are calculated as before:
Checking the MCV list, we find that the condition <literal>stringu1 &lt;
'IAAAAA'</> is satisfied by the first six entries and not the last four,
so the selectivity within the MCV part of the population is
<programlisting>
rows = 10000 * 0.00015104
= 2
selectivity = sum(relevant mvfs)
= 0.00333333 + 0.003 + 0.003 + 0.003 + 0.003 + 0.003
= 0.01833333
</programlisting>
Summing all the MCFs also tells us that the total fraction of the
population represented by MCVs is 0.03033333, and therefore the
fraction represented by the histogram is 0.96966667 (again, there
are no nulls, else we'd have to exclude them here). We can see
that the value <literal>IAAAAA</> falls nearly at the end of the
third histogram bucket. Using some rather cheesy assumptions
about the frequency of different characters, the planner arrives
at the estimate 0.298387 for the portion of the histogram population
that is less than <literal>IAAAAA</>. We then combine the estimates
for the MCV and non-MCV populations:
<programlisting>
selectivity = mcv_selectivity + histogram_selectivity * histogram_fraction
= 0.01833333 + 0.298387 * 0.96966667
= 0.307669
rows = 10000 * 0.307669
= 3077 (rounding off)
</programlisting>
In this particular example, the correction from the MCV list is fairly
small, because the column distribution is actually quite flat (the
statistics showing these particular values as being more common than
others are mostly due to sampling error). In a more typical case where
some values are significantly more common than others, this complicated
process gives a useful improvement in accuracy because the selectivity
for the most common values is found exactly.
</para>
<para>
Finally we will examine a query that includes a <literal>JOIN</literal>
together with a <literal>WHERE</literal> clause:
Now let's consider a case with more than one
condition in the <literal>WHERE</literal> clause:
<programlisting>
EXPLAIN SELECT * FROM tenk1 t1, tenk2 t2
WHERE t1.unique1 &lt; 50 AND t1.unique2 = t2.unique2;
EXPLAIN SELECT * FROM tenk1 WHERE unique1 &lt; 1000 AND stringu1 = 'xxx';
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 &lt; 50)
-> Index Scan using tenk2_unique2 on tenk2 t2 (cost=0.00..3.01 rows=1 width=244)
Index Cond: ("outer".unique2 = t2.unique2)
QUERY PLAN
--------------------------------------------------------------------------------
Bitmap Heap Scan on tenk1 (cost=23.80..396.91 rows=1 width=244)
Recheck Cond: (unique1 &lt; 1000)
Filter: (stringu1 = 'xxx'::name)
-&gt; Bitmap Index Scan on tenk1_unique1 (cost=0.00..23.80 rows=1007 width=0)
Index Cond: (unique1 &lt; 1000)
</programlisting>
The restriction on <classname>tenk1</classname>
<quote>unique1 &lt; 50</quote> is evaluated before the nested-loop join.
This is handled analogously to the previous range example. The restriction
operator for <literal>&lt;</literal> is <function>scalarlteqsel</function>
as before, but this time the value 50 is in the first bucket of the
<structfield>unique1</structfield> histogram:
The planner assumes that the two conditions are independent, so that
the individual selectivities of the clauses can be multiplied together:
<programlisting>
selectivity = selectivity(unique1 &lt; 1000) * selectivity(stringu1 = 'xxx')
= 0.100697 * 0.0014559
= 0.0001466
rows = 10000 * 0.0001466
= 1 (rounding off)
</programlisting>
Notice that the number of rows estimated to be returned from the bitmap
index scan reflects only the condition used with the index; this is
important since it affects the cost estimate for the subsequent heap
fetches.
</para>
<para>
Finally we will examine a query that involves a join:
<programlisting>
selectivity = (0 + (50 - bckt[1].min)/(bckt[1].max - bckt[1].min))/num_bckts
= (0 + (50 - 1)/(970 - 1))/10
= 0.005057
EXPLAIN SELECT * FROM tenk1 t1, tenk2 t2
WHERE t1.unique1 &lt; 50 AND t1.unique2 = t2.unique2;
rows = 10000 * 0.005057
= 51
QUERY PLAN
--------------------------------------------------------------------------------------
Nested Loop (cost=4.64..456.23 rows=50 width=488)
-&gt; Bitmap Heap Scan on tenk1 t1 (cost=4.64..142.17 rows=50 width=244)
Recheck Cond: (unique1 &lt; 50)
-&gt; Bitmap Index Scan on tenk1_unique1 (cost=0.00..4.63 rows=50 width=0)
Index Cond: (unique1 &lt; 50)
-&gt; Index Scan using tenk2_unique2 on tenk2 t2 (cost=0.00..6.27 rows=1 width=244)
Index Cond: (t2.unique2 = t1.unique2)
</programlisting>
The restriction for the join is:
The restriction on <structname>tenk1</structname>,
<literal>unique1 &lt; 50</literal>,
is evaluated before the nested-loop join.
This is handled analogously to the previous range example. This time the
value 50 falls into the first bucket of the
<structfield>unique1</structfield> histogram:
<programlisting>
t2.unique2 = t1.unique2
selectivity = (0 + (50 - bucket[1].min)/(bucket[1].max - bucket[1].min))/num_buckets
= (0 + (50 - 0)/(993 - 0))/10
= 0.005035
rows = 10000 * 0.005035
= 50 (rounding off)
</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>:
The restriction for the join is <literal>t2.unique2 = t1.unique2</>.
The operator is just
our familiar <literal>=</literal>, however the selectivity function is
obtained from the <structfield>oprjoin</structfield> column of
<structname>pg_operator</structname>, and is <function>eqjoinsel</function>.
<function>eqjoinsel</function> looks up the statistical information for both
<structname>tenk2</structname> and <structname>tenk1</structname>:
<programlisting>
SELECT tablename, null_frac,n_distinct, most_common_vals FROM pg_stats
WHERE tablename IN ('tenk1', 'tenk2') AND attname='unique2';
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
-----------+-----------+------------+------------------
@ -311,41 +390,62 @@ tablename | null_frac | n_distinct | most_common_vals
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
In this case there is no <acronym>MCV</acronym> information for
<structfield>unique2</structfield> because all the values appear to be
unique, so we 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)
= (1 - 0) * (1 - 0) / max(10000, 10000)
= 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
This is, subtract the null fraction from one for each of the relations,
and divide by the maximum of the numbers of distinct values.
The number of rows
that the join is likely to emit is calculated as the cardinality of the
Cartesian product of the two inputs, multiplied by the
selectivity:
<programlisting>
rows = (outer_cardinality * inner_cardinality) * selectivity
= (51 * 10000) * 0.0001
= 51
= (50 * 10000) * 0.0001
= 50
</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
Had there been MCV lists for the two columns,
<function>eqjoinsel</function> would have used direct comparison of the MCV
lists to determine the join selectivity within the part of the column
populations represented by the MCVs. The estimate for the remainder of the
populations follows the same approach shown here.
</para>
<para>
Notice that we showed <literal>inner_cardinality</> as 10000, that is,
the unmodified size of <structname>tenk2</>. It might appear from
inspection of the <command>EXPLAIN</> output that the estimate of
join rows comes from 50 * 1, that is, the number of outer rows times
the estimated number of rows obtained by each inner indexscan on
<structname>tenk2</>. But this is not the case: the join relation size
is estimated before any particular join plan has been considered. If
everything is working well then the two ways of estimating the join
size will produce about the same answer, but due to roundoff error and
other factors they sometimes diverge significantly.
</para>
<para>
For those interested in further details, estimation of the size of
a table (before any <literal>WHERE</> clauses) is done in
<filename>src/backend/optimizer/util/plancat.c</filename>. The generic
logic for clause selectivities is in
<filename>src/backend/optimizer/path/clausesel.c</filename>. The
operator-specific selectivity functions are mostly found
in <filename>src/backend/utils/adt/selfuncs.c</filename>.
</para>
</sect1>
</chapter>

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