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

that discussion.  Add a link from perform.sgml.

doc/src/sgml/perform.sgml

@@ -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>
@@ -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
+   <link linkend="catalog-pg-class"><structname>pg_class</structname></link>,
-   the columns <structfield>reltuples</structfield> and
+   in the columns <structfield>reltuples</structfield> and
    <structfield>relpages</structfield>.  We can look at it with
    queries similar to this one:
 
@@ -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
+   The amount of information stored in <structname>pg_statistic</structname>
-   <xref linkend="view-pg-stats">.
+   by <command>ANALYZE</>, in particular the maximum number of entries in the
-  </para>
-
-  <para>
-   The amount of information stored in <structname>pg_statistic</structname>,
-   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>

doc/src/sgml/planstats.sgml

@@ -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">
+   This chapter builds on the material covered in <xref
-   and <xref linkend="planner-stats">, and shows how the planner uses the 
+   linkend="using-explain"> and <xref linkend="planner-stats"> to show some
-   system statistics to estimate the number of rows each stage in a query might
+   additional details about how the planner uses the
-   return. This is a significant part of the planning / optimizing process,
+   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; 
+   The intent of this chapter is not to document the code in detail,
-   better done in the code itself, but to present an overview of how it works.
+   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
+   wishes to read the code.
-   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.
   </para>
 
  <sect1 id="row-estimation-examples">
@@ -33,65 +28,74 @@
   </indexterm>
 
   <para>
-   Using examples drawn from the regression test database, let's start with a 
+   The examples shown below use tables in the <productname>PostgreSQL</>
-   very simple query:
+   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>
+   How the planner determines the cardinality of <structname>tenk1</structname>
-   is covered in <xref linkend="using-explain">, but is repeated here for
+   is covered in <xref linkend="planner-stats">, but is repeated here for
-   completeness. The number of rows is looked up from 
+   completeness. The number of pages and rows is looked up in
-   <classname>pg_class</classname>:
+   <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
+      358 |     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
 </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
+                                   QUERY PLAN
-------------------------------------------------------------
+--------------------------------------------------------------------------------
- Seq Scan on tenk1  (cost=0.00..470.00 rows=1031 width=244)
+ Bitmap Heap Scan on tenk1  (cost=24.06..394.64 rows=1007 width=244)
-   Filter: (unique1 &lt; 1000)
+   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>
 
-   The planner examines the <literal>WHERE</literal> clause condition: 
+   The planner examines the <literal>WHERE</literal> clause condition
-
+   and looks up the selectivity function for the operator
-<programlisting>
+   <literal>&lt;</literal> in <structname>pg_operator</structname>.
-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>.
+   and the entry in this case is <function>scalarltsel</function>.
    The <function>scalarltsel</function> function retrieves the histogram for
-   <structfield>unique1</structfield> from <classname>pg_statistics</classname>
+   <structfield>unique1</structfield> from
-   - we can follow this by using the simpler <classname>pg_stats</classname> 
+   <structname>pg_statistics</structname>.  For manual queries it is more
+   convenient to look in the simpler <structname>pg_stats</structname>
    view:
 
 <programlisting>
@@ -100,7 +104,7 @@ 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>
@@ -108,81 +112,75 @@ WHERE tablename='tenk1' AND attname='unique1';
    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 
+   the second bucket (993-1997).  Assuming a linear distribution of
-   values inside each bucket we can calculate the selectivity as:
+   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
+selectivity = (1 + (1000 - bucket[2].min)/(bucket[2].max - bucket[2].min))/num_buckets
-            = (1 + (1000 - 970)/(1943 - 970))/10
+            = (1 + (1000 - 993)/(1997 - 993))/10
-            = 0.1031
+            = 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>:
+   <structname>tenk1</structname>:
 
 <programlisting>
 rows = rel_cardinality * selectivity
-     = 10000 * 0.1031
+     = 10000 * 0.100697
-     = 1031
+     = 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)
+ Seq Scan on tenk1  (cost=0.00..483.00 rows=30 width=244)
-   Filter: (stringu1 = 'ATAAAA'::name)
+   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
-<programlisting>
+   <function>eqsel</function>.  For equality estimation the histogram is
-stringu1 = 'ATAAAA'
+   not useful; instead the list of <firstterm>most
-</programlisting>
+   common values</> (<acronym>MCV</acronym>s) is used to determine the
-
+   selectivity. Let's have a look at the MCVs, with some additional columns
-   and looks up the restriction function for <literal>=</literal>, which is 
+   that will be useful later:
-   <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
 WHERE tablename='tenk1' AND attname='stringu1';
 
 null_frac         | 0
-n_distinct        | 672
+n_distinct        | 676
-most_common_vals  | {FDAAAA,NHAAAA,ATAAAA,BGAAAA,EBAAAA,MOAAAA,NDAAAA,OWAAAA,BHAAAA,BJAAAA}
+most_common_vals  | {EJAAAA,BBAAAA,CRAAAA,FCAAAA,FEAAAA,GSAAAA,JOAAAA,MCAAAA,NAAAAA,WGAAAA}
-most_common_freqs | {0.00333333,0.00333333,0.003,0.003,0.003,0.003,0.003,0.003,0.00266667,0.00266667}
+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>)
+   Since <literal>CRAAAA</> appears in the list of MCVs, the selectivity is
-   corresponding to the third <acronym>MCV</acronym> &mdash; 'ATAAAA': 
+   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 
+   As before, the estimated number of rows is just the product of this with the
-   cardinality of <classname>tenk1</classname> as before:
+   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>
@@ -194,11 +192,11 @@ 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
+   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
@@ -206,100 +204,181 @@ EXPLAIN SELECT * FROM tenk1 WHERE stringu1 = 'xxx';
 
 <programlisting>
 selectivity = (1 - sum(mvf))/(num_distinct - num_mcv)
-            = (1 - (0.00333333 + 0.00333333 + 0.003 + 0.003 + 0.003 
+            = (1 - (0.00333333 + 0.003 + 0.003 + 0.003 + 0.003 + 0.003 +
-            + 0.003 + 0.003 + 0.003 + 0.00266667 + 0.00266667))/(672 - 10)
+                    0.003 + 0.003 + 0.003 + 0.003))/(676 - 10)
-            = 0.001465
+            = 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 
+   subtract them from one, then
-   of these, and divide by the <emphasis>remaining</emphasis> distinct values. 
+   divide by the number of <emphasis>other</emphasis> distinct values.
-   Notice that there are no null values so we don't have to worry about those. 
+   This amounts to assuming that the fraction of the column that is not any
-   The estimated number of rows is calculated as usual:
+   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
+rows = 10000 * 0.0014559
-     = 15
+     = 15  (rounding off)
 </programlisting>
-
   </para>
 
   <para>
-   Let's increase the complexity to consider a case with more than one 
+   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 stringu1 &lt; 'IAAAAA';
+
+                         QUERY PLAN
+------------------------------------------------------------
+ Seq Scan on tenk1  (cost=0.00..483.00 rows=3077 width=244)
+   Filter: (stringu1 &lt; 'IAAAAA'::name)
+</programlisting>
+
+   We already saw the MCV information for <structfield>stringu1</>,
+   and here is its histogram:
+
+<programlisting>
+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>
+
+   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>
+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>
+   Now let's consider a case with more than one
    condition in the <literal>WHERE</literal> clause:
 
 <programlisting>
 EXPLAIN SELECT * FROM tenk1 WHERE unique1 &lt; 1000 AND stringu1 = 'xxx';
 
-                       QUERY PLAN
+                                   QUERY PLAN
------------------------------------------------------------
+--------------------------------------------------------------------------------
- Seq Scan on tenk1  (cost=0.00..495.00 rows=2 width=244)
+ Bitmap Heap Scan on tenk1  (cost=23.80..396.91 rows=1 width=244)
-   Filter: ((unique1 &lt; 1000) AND (stringu1 = 'xxx'::name))
+   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>
 
-   An assumption of independence is made and the selectivities of the 
+   The planner assumes that the two conditions are independent, so that
-   individual restrictions are multiplied together:
+   the individual selectivities of the clauses can be multiplied together:
 
 <programlisting>
 selectivity = selectivity(unique1 &lt; 1000) * selectivity(stringu1 = 'xxx')
-            = 0.1031 * 0.001465
+            = 0.100697 * 0.0014559
-            = 0.00015104
+            = 0.0001466
+
+rows        = 10000 * 0.0001466
+            = 1  (rounding off)
 </programlisting>
 
-   The row estimates are calculated as before:
+   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
-<programlisting>
+   important since it affects the cost estimate for the subsequent heap
-rows = 10000 * 0.00015104
+   fetches.
-     = 2
-</programlisting>
   </para>
 
   <para>
-   Finally we will examine a query that includes a <literal>JOIN</literal> 
+   Finally we will examine a query that involves a join:
-   together with a <literal>WHERE</literal> clause:
 
 <programlisting>
-EXPLAIN SELECT *  FROM tenk1 t1, tenk2 t2 
+EXPLAIN SELECT * FROM tenk1 t1, tenk2 t2
 WHERE t1.unique1 &lt; 50 AND t1.unique2 = t2.unique2;
 
                                       QUERY PLAN
------------------------------------------------------------------------------------------
+--------------------------------------------------------------------------------------
- Nested Loop  (cost=0.00..346.90 rows=51 width=488)
+ Nested Loop  (cost=4.64..456.23 rows=50 width=488)
-   ->  Index Scan using tenk1_unique1 on tenk1 t1  (cost=0.00..192.57 rows=51 width=244)
+   -&gt;  Bitmap Heap Scan on tenk1 t1  (cost=4.64..142.17 rows=50 width=244)
-         Index Cond: (unique1 &lt; 50)
+         Recheck Cond: (unique1 &lt; 50)
-   ->  Index Scan using tenk2_unique2 on tenk2 t2  (cost=0.00..3.01 rows=1 width=244)
+         -&gt;  Bitmap Index Scan on tenk1_unique1  (cost=0.00..4.63 rows=50 width=0)
-         Index Cond: ("outer".unique2 = t2.unique2)
+               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 on <classname>tenk1</classname> 
+   The restriction on <structname>tenk1</structname>,
-   <quote>unique1 &lt; 50</quote> is evaluated before the nested-loop join. 
+   <literal>unique1 &lt; 50</literal>,
-   This is handled analogously to the previous range example. The restriction 
+   is evaluated before the nested-loop join.
-   operator for <literal>&lt;</literal> is <function>scalarlteqsel</function> 
+   This is handled analogously to the previous range example.  This time the
-   as before, but this time the value 50 is in the first bucket of the 
+   value 50 falls into the first bucket of the
    <structfield>unique1</structfield> histogram:
 
 <programlisting>
-selectivity = (0 + (50 - bckt[1].min)/(bckt[1].max - bckt[1].min))/num_bckts
+selectivity = (0 + (50 - bucket[1].min)/(bucket[1].max - bucket[1].min))/num_buckets
-            = (0 + (50 - 1)/(970 - 1))/10
+            = (0 + (50 - 0)/(993 - 0))/10
-            = 0.005057
+            = 0.005035
 
-rows        = 10000 * 0.005057
+rows        = 10000 * 0.005035
-            = 51
+            = 50  (rounding off)
 </programlisting>
 
-   The restriction for the join is:
+   The restriction for the join is <literal>t2.unique2 = t1.unique2</>.
-
+   The operator is just
-<programlisting>
+   our familiar <literal>=</literal>, however the selectivity function is
-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>.
+   <structname>pg_operator</structname>, and is <function>eqjoinsel</function>.
-   Additionally we use the statistical information for both 
+   <function>eqjoinsel</function> looks up the statistical information for both
-   <classname>tenk2</classname> and <classname>tenk1</classname>:
+   <structname>tenk2</structname> and <structname>tenk1</structname>:
 
 <programlisting>
 SELECT tablename, null_frac,n_distinct, most_common_vals FROM pg_stats
@@ -313,39 +392,60 @@ tablename  | null_frac | n_distinct | most_common_vals
 
    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 
+   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 
+   and divide by the maximum of the numbers of distinct values.
-   that the join is likely to emit is calculated as the cardinality of 
+   The number of rows
-   Cartesian product of the two nodes in the nested-loop, multiplied by the 
+   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
+     = (50 * 10000) * 0.0001
-     = 51
+     = 50
 </programlisting>
   </para>
 
   <para>
-   For those interested in further details, estimation of the number of rows in
+   Had there been MCV lists for the two columns,
-   a relation is covered in 
+   <function>eqjoinsel</function> would have used direct comparison of the MCV
-   <filename>src/backend/optimizer/util/plancat.c</filename>. The calculation
+   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 actual
+   <filename>src/backend/optimizer/path/clausesel.c</filename>.  The
-   implementations of the operator and join restriction functions can be found 
+   operator-specific selectivity functions are mostly found
    in <filename>src/backend/utils/adt/selfuncs.c</filename>.
   </para>
 
  </sect1>
 
-
 </chapter>