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<h1 align='center'> The SQLite Query Planner</h1><p>
  This document provides overview of how the query planner and optimizer
  for SQLite works.
</p>
<p>
  Given a single SQL statement, there might be dozens, hundreds, or even
  thousands of ways to implement that statement, depending on the complexity
  of the statement itself and of the underlying database schema.  The 
  task of the query planner is to select an algorithm from among the many
  choices that provides the answer with a minimum of disk I/O and CPU
  overhead.
</p>
<p>
  With release 3.8.0, the SQLite query planner was reimplemented as the
  <a href="queryplanner-ng.html">Next Generation Query Planner</a> or "NGQP".  All of the features, techniques,
  and algorithms described in this document are applicable to both the
  pre-3.8.0 legacy query planner and to the NGQP.  For further information on
  how the NGQP differs from the legacy query planner, see the 
  <a href="queryplanner-ng.html">detailed description of the NGQP</a>.
</p>
<a name="where_clause"></a>
<h2>1.0 WHERE clause analysis</h2><p>
  The WHERE clause on a query is broken up into "terms" where each term
  is separated from the others by an AND operator.
  If the WHERE clause is composed of constraints separate by the OR
  operator then the entire clause is considered to be a single "term"
  to which the <a href="#or_opt">OR-clause optimization</a> is applied.
</p>
<p>
  All terms of the WHERE clause are analyzed to see if they can be
  satisfied using indices.
  To be usable by an index a term must be of one of the following
  forms:
</p>
<blockquote><pre><b>
  </b><i>column</i><b> = </b><i>expression</i><b>
  </b><i>column</i><b> &gt; </b><i>expression</i><b>
  </b><i>column</i><b> &gt;= </b><i>expression</i><b>
  </b><i>column</i><b> &lt; </b><i>expression</i><b>
  </b><i>column</i><b> &lt;= </b><i>expression</i><b>
  </b><i>expression</i><b> = </b><i>column</i><b>
  </b><i>expression</i><b> &gt; </b><i>column</i><b>
  </b><i>expression</i><b> &gt;= </b><i>column</i><b>
  </b><i>expression</i><b> &lt; </b><i>column</i><b>
  </b><i>expression</i><b> &lt;= </b><i>column</i><b>
  </b><i>column</i><b> IN (</b><i>expression-list</i><b>)
  </b><i>column</i><b> IN (</b><i>subquery</i><b>)
  </b><i>column</i><b> IS NULL
</b></pre></blockquote><p>
  If an index is created using a statement like this:
</p>
<blockquote><pre>
  CREATE INDEX idx_ex1 ON ex1(a,b,c,d,e,...,y,z);
</pre></blockquote><p>
  Then the index might be used if the initial columns of the index
  (columns a, b, and so forth) appear in WHERE clause terms.
  The initial columns of the index must be used with
  the <tt><b><big>=</big></b></tt> or <tt><b><big>IN</big></b></tt> or <tt><b><big>IS NULL</big></b></tt> operators.  
  The right-most column that is used can employ inequalities.  
  For the right-most
  column of an index that is used, there can be up to two inequalities
  that must sandwich the allowed values of the column between two extremes.
</p>
<p>
  It is not necessary for every column of an index to appear in a
  WHERE clause term in order for that index to be used. 
  But there can not be gaps in the columns of the index that are used.
  Thus for the example index above, if there is no WHERE clause term
  that constraints column c, then terms that constrain columns a and b can
  be used with the index but not terms that constraint columns d through z.
  Similarly, index columns will not normally be used (for indexing purposes)
  if they are to the right of a 
  column that is constrained only by inequalities.
  (See the <a href="optoverview.html#skipscan">skip-scan optimization</a> below for the exception.)
</p>
<a name="idxexamp"></a>
<h3>1.1 Index term usage examples</h3><p>
  For the index above and WHERE clause like this:
</p>
<blockquote><pre>
  ... WHERE a=5 AND b IN (1,2,3) AND c IS NULL AND d='hello'
</pre></blockquote><p>
  The first four columns a, b, c, and d of the index would be usable since
  those four columns form a prefix of the index and are all bound by
  equality constraints.
</p>
<p>
  For the index above and WHERE clause like this:
</p>
<blockquote><pre>
  ... WHERE a=5 AND b IN (1,2,3) AND c>12 AND d='hello'
</pre></blockquote><p>
  Only columns a, b, and c of the index would be usable.  The d column
  would not be usable because it occurs to the right of c and c is
  constrained only by inequalities.
</p>
<p>
  For the index above and WHERE clause like this:
</p>
<blockquote><pre>
  ... WHERE a=5 AND b IN (1,2,3) AND d='hello'
</pre></blockquote><p>
  Only columns a and b of the index would be usable.  The d column
  would not be usable because column c is not constrained and there can
  be no gaps in the set of columns that usable by the index.
</p>
<p>
  For the index above and WHERE clause like this:
</p>
<blockquote><pre>
  ... WHERE b IN (1,2,3) AND c NOT NULL AND d='hello'
</pre></blockquote><p>
  The index is not usable at all because the left-most column of the
  index (column "a") is not constrained.  Assuming there are no other
  indices, the query above would result in a full table scan.
</p>
<p>
  For the index above and WHERE clause like this:
</p>
<blockquote><pre>
  ... WHERE a=5 OR b IN (1,2,3) OR c NOT NULL OR d='hello'
</pre></blockquote><p>
  The index is not usable because the WHERE clause terms are connected
  by OR instead of AND. This query would result in a full table scan.
  However, if three additional indices where added that contained columns
  b, c, and d as their left-most columns, then the
  <a href="#or_opt">OR-clause optimization</a> might apply.
</p>
<a name="between_opt"></a>
<h2>2.0 The BETWEEN optimization</h2><p>
  If a term of the WHERE clause is of the following form:
</p>
<blockquote><pre><b>
  </b><i>expr1</i><b> BETWEEN </b><i>expr2</i><b> AND </b><i>expr3</i><b>
</b></pre></blockquote><p>
  Then two "virtual" terms are added as follows:
</p>
<blockquote><pre><b>
  </b><i>expr1</i><b> &gt;= </b><i>expr2</i><b> AND </b><i>expr1</i><b> &lt;= </b><i>expr3</i><b>
</b></pre></blockquote><p>
  Virtual terms are used for analysis only and do not cause any VDBE
  code to be generated.
  If both virtual terms end up being used as constraints on an index,
  then the original BETWEEN term is omitted and the corresponding test
  is not performed on input rows.
  Thus if the BETWEEN term ends up being used as an index constraint
  no tests are ever performed on that term.
  On the other hand, the
  virtual terms themselves never causes tests to be performed on
  input rows.
  Thus if the BETWEEN term is not used as an index constraint and
  instead must be used to test input rows, the <i>expr1</i> expression is
  only evaluated once.
</p>
<a name="or_opt"></a>
<h2>3.0 OR optimizations</h2><p>
  WHERE clause constraints that are connected by OR instead of AND can
  be handled in two different ways.
  If a term consists of multiple subterms containing a common column
  name and separated by OR, like this:
</p>
<blockquote><pre><b>
  </b><i>column</i><b> = </b><i>expr1</i><b> OR </b><i>column</i><b> = </b><i>expr2</i><b> OR </b><i>column</i><b> = </b><i>expr3</i><b> OR ...
</b></pre></blockquote><p>
  Then that term is rewritten as follows:
</p>
<blockquote><pre><b>
  </b><i>column</i><b> IN (</b><i>expr1</i><b>,</b><i>expr2</i><b>,</b><i>expr3</i><b>,...)
</b></pre></blockquote><p>
  The rewritten term then might go on to constrain an index using the
  normal rules for <tt><b><big>IN</big></b></tt> operators.  Note that <i>column</i> must be
  the same column in every OR-connected subterm,
  although the column can occur on either the left or the right side of
  the <tt><b><big>=</big></b></tt> operator.
</p>
<p>
  If and only if the previously described conversion of OR to an IN operator
  does not work, the second OR-clause optimization is attempted.
  Suppose the OR clause consists of multiple subterms as follows:
</p>
<blockquote><pre><b>
  </b><i>expr1</i><b> OR </b><i>expr2</i><b> OR </b><i>expr3</i><b>
</b></pre></blockquote><p>
  Individual subterms might be a single comparison expression like
  <tt><b><big>a=5</big></b></tt> or <tt><b><big>x>y</big></b></tt> or they can be LIKE or BETWEEN expressions, or a subterm
  can be a parenthesized list of AND-connected sub-subterms.
  Each subterm is analyzed as if it were itself the entire WHERE clause
  in order to see if the subterm is indexable by itself.
  If <u>every</u> subterm of an OR clause is separately indexable
  then the OR clause might be coded such that a separate index is used
  to evaluate each term of the OR clause.  One way to think about how
  SQLite uses separate indices for each OR clause term is to imagine
  that the WHERE clause where rewritten as follows:
</p>
<blockquote><pre><b>
  rowid IN (SELECT rowid FROM </b><i>table</i><b> WHERE </b><i>expr1</i><b>
            UNION SELECT rowid FROM </b><i>table</i><b> WHERE </b><i>expr2</i><b>
            UNION SELECT rowid FROM </b><i>table</i><b> WHERE </b><i>expr3</i><b>)
</b></pre></blockquote><p>
  The rewritten expression above is conceptual; WHERE clauses containing
  OR are not really rewritten this way.
  The actual implementation of the OR clause uses a mechanism that is
  more efficient than subqueries and which works even 
  for tables where the "rowid" column name has been 
  overloaded for other uses and no longer refers to the real rowid.
  But the essence of the implementation is captured by the statement
  above:  Separate indices are used to find candidate result rows
  from each OR clause term and the final result is the union of
  those rows.
</p>
<p>
  Note that in most cases, SQLite will only use a single index for each
  table in the FROM clause of a query.  The second OR-clause optimization
  described here is the exception to that rule.  With an OR-clause,
  a different index might be used for each subterm in the OR-clause.
</p>
<p>
  For any given query, the fact that the OR-clause optimization described
  here can be used does not guarantee that it will be used.
  SQLite uses a cost-based query planner that estimates the CPU and
  disk I/O costs of various competing query plans and chooses the plan
  that it thinks will be the fastest.  If there are many OR terms in
  the WHERE clause or if some of the indices on individual OR-clause 
  subterms are not very selective, then SQLite might decide that it is
  faster to use a different query algorithm, or even a full-table scan.
  Application developers can use the
  <a href="lang_explain.html">EXPLAIN QUERY PLAN</a> prefix on a statement to get a
  high-level overview of the chosen query strategy.
</p>
<a name="like_opt"></a>
<h2>4.0 The LIKE optimization</h2><p>
  Terms that are composed of the <a href="lang_expr.html#like">LIKE</a> or <a href="lang_expr.html#glob">GLOB</a> operator
  can sometimes be used to constrain indices.
  There are many conditions on this use:
</p>
<p>
  <ol>
  <li>The left-hand side of the LIKE or GLOB operator must be the name
      of an indexed column with <a href="datatype3.html#affinity">TEXT affinity</a>.</li>
  <li>The right-hand side of the LIKE or GLOB must be either a string literal
      or a <a href="lang_expr.html#varparam">parameter</a> bound to a string literal
      that does not begin with a wildcard character.</li>
  <li>The ESCAPE clause cannot appear on the LIKE operator.</li>
  <li>The built-in functions used to implement LIKE and GLOB must not
      have been overloaded using the sqlite3_create_function() API.</li>
  <li>For the GLOB operator, the column must be indexed using the 
      built-in BINARY collating sequence.</li>
  <li>For the LIKE operator, if <a href="pragma.html#pragma_case_sensitive_like">case_sensitive_like</a> mode is enabled then
      the column must indexed using BINARY collating sequence, or if
      <a href="pragma.html#pragma_case_sensitive_like">case_sensitive_like</a> mode is disabled then the column must indexed
      using built-in NOCASE collating sequence.</li>
  </ol>
</p>
<p>
  The LIKE operator has two modes that can be set by a
  <a href="pragma.html#pragma_case_sensitive_like">pragma</a>.  The
  default mode is for LIKE comparisons to be insensitive to differences
  of case for latin1 characters.  Thus, by default, the following
  expression is true:
</p>
<blockquote><pre>
  'a' LIKE 'A'
</pre></blockquote><p>
  But if the case_sensitive_like pragma is enabled as follows:
</p>
<blockquote><pre>
  PRAGMA case_sensitive_like=ON;
</pre></blockquote><p>
  Then the LIKE operator pays attention to case and the example above would
  evaluate to false.  Note that case insensitivity only applies to
  latin1 characters - basically the upper and lower case letters of English
  in the lower 127 byte codes of ASCII.  International character sets
  are case sensitive in SQLite unless an application-defined
  <a href="datatype3.html#collation">collating sequence</a> and <a href="lang_corefunc.html#like">like() SQL function</a> are provided that
  take non-ASCII characters into account.
  But if an application-defined collating sequence and/or like() SQL
  function are provided, the LIKE optimization described here will never
  be taken.
</p>
<p>
  The LIKE operator is case insensitive by default because this is what
  the SQL standard requires.  You can change the default behavior at
  compile time by using the <a href="compile.html#case_sensitive_like">SQLITE_CASE_SENSITIVE_LIKE</a> command-line option
  to the compiler.
</p>
<p>
  The LIKE optimization might occur if the column named on the left of the
  operator is indexed using the built-in BINARY collating sequence and
  case_sensitive_like is turned on.  Or the optimization might occur if
  the column is indexed using the built-in NOCASE collating sequence and the 
  case_sensitive_like mode is off.  These are the only two combinations
  under which LIKE operators will be optimized.
</p>
<p>
  The GLOB operator is always case sensitive.  The column on the left side
  of the GLOB operator must always use the built-in BINARY collating sequence
  or no attempt will be made to optimize that operator with indices.
</p>
<p>
  The LIKE optimization will only be attempted if
  the right-hand side of the GLOB or LIKE operator is either
  literal string or a <a href="lang_expr.html#varparam">parameter</a> that has been <a href="c3ref/bind_blob.html">bound</a>
  to a string literal.  The string literal must not
  begin with a wildcard; if the right-hand side begins with a wildcard
  character then this optimization is attempted.  If the right-hand side 
  is a <a href="lang_expr.html#varparam">parameter</a> that is bound to a string, then this optimization is
  only attempted if the <a href="c3ref/stmt.html">prepared statement</a> containing the expression
  was compiled with <a href="c3ref/prepare.html">sqlite3_prepare_v2()</a> or <a href="c3ref/prepare.html">sqlite3_prepare16_v2()</a>.
  The LIKE optimization is not attempted if the
  right-hand side is a <a href="lang_expr.html#varparam">parameter</a> and the statement was prepared using
  <a href="c3ref/prepare.html">sqlite3_prepare()</a> or <a href="c3ref/prepare.html">sqlite3_prepare16()</a>.
  The LIKE optimization is not attempted if there is an EXCEPT phrase
  on the LIKE operator.
</p>
<p>
  Suppose the initial sequence of non-wildcard characters on the right-hand
  side of the LIKE or GLOB operator is <i>x</i>.  We are using a single 
  character to denote this non-wildcard prefix but the reader should
  understand that the prefix can consist of more than 1 character.
  Let <i>y</i> be the smallest string that is the same length as /x/ but which
  compares greater than <i>x</i>.  For example, if <i>x</i> is <tt><b><big>hello</big></b></tt> then
  <i>y</i> would be <tt><b><big>hellp</big></b></tt>.
  The LIKE and GLOB optimizations consist of adding two virtual terms
  like this:
</p>
<blockquote><pre><b>
  </b><i>column</i><b> &gt;= </b><i>x</i><b> AND </b><i>column</i><b> &lt; </b><i>y</i><b>
</b></pre></blockquote><p>
  Under most circumstances, the original LIKE or GLOB operator is still
  tested against each input row even if the virtual terms are used to
  constrain an index.  This is because we do not know what additional
  constraints may be imposed by characters to the right
  of the <i>x</i> prefix.  However, if there is only a single
  global wildcard to the right of <i>x</i>, then the original LIKE or 
  GLOB test is disabled.
  In other words, if the pattern is like this:
</p>
<blockquote><pre><b>
  </b><i>column</i><b> LIKE </b><i>x</i><b>%
  </b><i>column</i><b> GLOB </b><i>x</i><b>*
</b></pre></blockquote><p>
  then the original LIKE or GLOB tests are disabled when the virtual
  terms constrain an index because in that case we know that all of the
  rows selected by the index will pass the LIKE or GLOB test.
</p>
<p>
  Note that when the right-hand side of a LIKE or GLOB operator is
  a <a href="lang_expr.html#varparam">parameter</a> and the statement is prepared using <a href="c3ref/prepare.html">sqlite3_prepare_v2()</a>
  or <a href="c3ref/prepare.html">sqlite3_prepare16_v2()</a> then the statement is automatically reparsed
  and recompiled on the first <a href="c3ref/step.html">sqlite3_step()</a> call of each run if the binding
  to the right-hand side parameter has changed since the previous run.
  This reparse and recompile is essentially the same action that occurs
  following a schema change.  The recompile is necessary so that the query
  planner can examine the new value bound to the right-hand side of the
  LIKE or GLOB operator and determine whether or not to employ the
  optimization described above.
</p>
<a name="skipscan"></a>
<h2>5.0 The Skip-Scan Optimization</h2><p>
  The general rule is that indexes are only useful if there are 
  WHERE-clause constraints on the left-most columns of the index.
  However, in some cases,
  SQLite is able to use an index even if the first few columns of
  the index are omitted from the WHERE clause but later columns 
  are included.
</p>
<p>
  Consider a table such as the following:
</p>
<blockquote><pre>
  CREATE TABLE people(
    name TEXT PRIMARY KEY,
    role TEXT NOT NULL,
    height INT NOT NULL, -- in cm
    CHECK( role IN ('student','teacher') )
  );
  CREATE INDEX people_idx1 ON people(role, height);
</pre></blockquote><p>
  The people table has one entry for each person in a large
  organization.  Each person is either a "student" or a "teacher",
  as determined by the "role" field.  And we record the height in
  centimeters of each person.  The role and height are indexed.
  Notice that the left-most column of the index is not very
  selective - it only contains two possible values.
</p>
<p>
  Now consider a query to find the names of everyone in the
  organization that is 180cm tall or taller:
</p>
<blockquote><pre>
  SELECT name FROM people WHERE height>=180;
</pre></blockquote><p>
  Because the left-most column of the index does not appear in the
  WHERE clause of the query, one is tempted to conclude that the
  index is not usable here.  But SQLite is able to use the index.
  Conceptually, SQLite uses the index as if the query were more
  like the following:
</p>
<blockquote><pre>
  SELECT name FROM people
   WHERE role IN (SELECT DISTINCT role FROM people)
     AND height>=180;
</pre></blockquote><p>
  Or this:
</p>
<blockquote><pre>
  SELECT name FROM people WHERE role='teacher' AND height>=180
  UNION ALL
  SELECT name FROM people WHERE role='student' AND height>=180;
</pre></blockquote><p>
  The alternative query formulations shown above are conceptual only.
  SQLite does not really transform the query. 
  The actual query plan is like this:
  SQLite locates the first possible value for "role", which it
  can do by rewinding the "people_idx1" index to the beginning and reading
  the first record.  SQLite stores this first "role" value in an
  internal variable that we will here call "$role".  Then SQLite
  runs a query like: "SELECT name FROM people WHERE role=$role AND height>=180".
  This query has an equality constraint on the left-most column of the
  index and so the index can be used to resolve that query.  Once
  that query is finished, SQLite then uses the "people_idx1" index to
  locate the next value of the "role" column, using code that is logically
  similar to "SELECT role FROM people WHERE role>$role LIMIT 1".
  This new "role" value overwrites the $role variable, and the process
  repeats until all possible values for "role" have been examined.
</p>
<p>
  We call this kind of index usage a "skip-scan" because the database
  engine is basically doing a full scan of the index but it optimizes the
  scan (making it less than "full") by occasionally skipping ahead to the
  next candidate value.
</p>
<p>
  SQLite might use a skip-scan on an index if it knows that the first
  one or more columns contain many duplication values.
  If there are too few duplicates
  in the left-most columns of the index, then it would
  be faster to simply step ahead to the next value, and thus do
  a full table scan, than to do a binary search on an index to locate
  the next left-column value.
</p>
<p>
  The only way that SQLite can know that the left-most columns of an index
  have many duplicate is if the <a href="lang_analyze.html">ANALYZE</a> command has been run
  on the database.
  Without the results of ANALYZE, SQLite has to guess at the "shape" of
  the data in the table, and the default guess is that there are an average
  of 10 duplicates for every value in the left-most column of the index.
  But skip-scan only becomes profitable (it only gets to be faster than
  a full table scan) when the number of duplicates is about 18 or more.
  Hence, a skip-scan is never used on a database that has not been analyzed.
</p>
<a name="joins"></a>
<h2>6.0 Joins</h2><p>
  The ON and USING clauses of an inner join are converted into additional
  terms of the WHERE clause prior to WHERE clause analysis described
  above in paragraph 1.0.  Thus with SQLite, there is no computational
  advantage to use the newer SQL92 join syntax
  over the older SQL89 comma-join syntax.  They both end up accomplishing
  exactly the same thing on inner joins.
</p>
<p>
  For a LEFT OUTER JOIN the situation is more complex.  The following
  two queries are not equivalent:
</p>
<blockquote><pre>
  SELECT * FROM tab1 LEFT JOIN tab2 ON tab1.x=tab2.y;
  SELECT * FROM tab1 LEFT JOIN tab2 WHERE tab1.x=tab2.y;
</pre></blockquote><p>
  For an inner join, the two queries above would be identical.  But
  special processing applies to the ON and USING clauses of an OUTER join:
  specifically, the constraints in an ON or USING clause do not apply if
  the right table of the join is on a null row, but the constraints do apply
  in the WHERE clause.  The net effect is that putting the ON or USING
  clause expressions for a LEFT JOIN in the WHERE clause effectively converts
  the query to an
  ordinary INNER JOIN - albeit an inner join that runs more slowly.
</p>
<a name="table_order"></a>
<h3>6.1 Order of tables in a join</h3><p>
  The current implementation of 
  SQLite uses only loop joins.  That is to say, joins are implemented as
  nested loops.
</p>
<p>
  The default order of the nested loops in a join is for the left-most
  table in the FROM clause to form the outer loop and the right-most
  table to form the inner loop.
  However, SQLite will nest the loops in a different order if doing so
  will help it to select better indices.
</p>
<p>
  Inner joins can be freely reordered.  However a left outer join is
  neither commutative nor associative and hence will not be reordered.
  Inner joins to the left and right of the outer join might be reordered
  if the optimizer thinks that is advantageous but the outer joins are
  always evaluated in the order in which they occur.
</p>
<p>
  SQLite <a href="lang_select.html#crossjoin">treats the CROSS JOIN operator specially</a>.
  The CROSS JOIN operator is commutative in theory.  But SQLite chooses to
  never reorder tables in a CROSS JOIN.  This provides a mechanism
  by which the programmer can force SQLite to choose a particular loop nesting
  order.  
</p>
<p>
  When selecting the order of tables in a join, SQLite uses an efficient
  polynomial-time algorithm.  Because of this,
  SQLite is able to plan queries with 50- or 60-way joins in a matter of
  microseconds.
</p>
<p>
  Join reordering is automatic and usually works well enough that
  programmers do not have to think about it, especially if <a href="lang_analyze.html">ANALYZE</a>
  has been used to gather statistics about the available indices.
  But occasionally some hints from the programmer are needed.
  Consider, for example, the following schema:
</p>
<blockquote><pre>
  CREATE TABLE node(
     id INTEGER PRIMARY KEY,
     name TEXT
  );
  CREATE INDEX node_idx ON node(name);
  CREATE TABLE edge(
     orig INTEGER REFERENCES node,
     dest INTEGER REFERENCES node,
     PRIMARY KEY(orig, dest)
  );
  CREATE INDEX edge_idx ON edge(dest,orig);
</pre></blockquote><p>
  The schema above defines a directed graph with the ability to store a
  name at each node. Now consider a query against this schema:
</p>
<blockquote><pre>
  SELECT *
    FROM edge AS e,
         node AS n1,
         node AS n2
   WHERE n1.name = 'alice'
     AND n2.name = 'bob'
     AND e.orig = n1.id
     AND e.dest = n2.id;
</pre></blockquote><p>
  This query asks for is all information about edges that go from
  nodes labeled "alice" to nodes labeled "bob".
  The query optimizer in SQLite has basically two choices on how to
  implement this query.  (There are actually six different choices, but
  we will only consider two of them here.)
  Pseudocode below demonstrating these two choices.
</p>
<a name="option1"></a>
<p>Option 1:</p>
<blockquote><pre>
  foreach n1 where n1.name='alice' do:
    foreach n2 where n2.name='bob' do:
      foreach e where e.orig=n1.id and e.dest=n2.id
        return n1.*, n2.*, e.*
      end
    end
  end
</pre></blockquote><a name="option2"></a>
<p>Option 2:</p>
<blockquote><pre>
  foreach n1 where n1.name='alice' do:
    foreach e where e.orig=n1.id do:
      foreach n2 where n2.id=e.dest and n2.name='bob' do:
        return n1.*, n2.*, e.*
      end
    end
  end
</pre></blockquote><p>
  The same indices are used to speed up every loop in both implementation
  options.
  The only difference in these two query plans is the order in which
  the loops are nested.
</p>
<p>
  So which query plan is better? It turns out that the answer depends on
  what kind of data is found in the node and edge tables.
</p>
<p>
  Let the number of alice nodes be M and the number of bob nodes be N.
  Consider two scenarios. In the first scenario, M and N are both 2 but
  there are thousands of edges on each node. In this case, option 1 is
  preferred. With option 1, the inner loop checks for the existence of
  an edge between a pair of nodes and outputs the result if found. 
  But because there are only 2 alice and bob nodes each, the inner loop
  only has to run 4 times and the query is very quick. Option 2 would
  take much longer here. The outer loop of option 2 only executes twice,
  but because there are a large number of edges leaving each alice node,
  the middle loop has to iterate many thousands of times. It will be
  much slower. So in the first scenario, we prefer to use option 1.
</p>
<p>
  Now consider the case where M and N are both 3500. Alice nodes are
  abundant. But suppose each of these nodes is connected by only one
  or two edges. In this case, option 2 is preferred. With option 2,
  the outer loop still has to run 3500 times, but the middle loop only
  runs once or twice for each outer loop and the inner loop will only
  run once for each middle loop, if at all. So the total number of
  iterations of the inner loop is around 7000. Option 1, on the other
  hand, has to run both its outer loop and its middle loop 3500 times
  each, resulting in 12 million iterations of the middle loop.
  Thus in the second scenario, option 2 is nearly 2000 times faster
  than option 1.
</p>
<p>
  So you can see that depending on how the data is structured in the table,
  either query plan 1 or query plan 2 might be better.  Which plan does
  SQLite choose by default?  As of version 3.6.18, without running <a href="lang_analyze.html">ANALYZE</a>,
  SQLite will choose option 2.
  But if the <a href="lang_analyze.html">ANALYZE</a> command is run in order to gather statistics,
  a different choice might be made if the statistics indicate that the
  alternative is likely to run faster.
</p>
<a name="manctrl"></a>
<h3>6.2 Manual Control Of Query Plans Using SQLITE_STAT Tables</h3><p>
  SQLite provides the ability for advanced programmers to exercise control
  over the query plan chosen by the optimizer. One method for doing this
  is to fudge the <a href="lang_analyze.html">ANALYZE</a> results in the <a href="fileformat2.html#stat1tab">sqlite_stat1</a>, 
  <a href="fileformat2.html#stat3tab">sqlite_stat3</a>, and/or <a href="fileformat2.html#stat4tab">sqlite_stat4</a> tables.  That approach is not 
  recommended except for the one scenario described in the next paragraph.
</p>
<p>
  For a program that uses an SQLite database as its 
  <a href="appfileformat.html">application file-format</a>,
  when a new database instance is first created the <a href="lang_analyze.html">ANALYZE</a>
  command is ineffective because the database contain no data from which
  to gather statistics.  In that case, one could construct a large prototype
  database containing typical data during development and run the 
  <a href="lang_analyze.html">ANALYZE</a> command on this prototype database to gather statistics,
  then save the prototype statistics as part of the application.
  After deployment, when the application goes to create a new database file,
  it can run the <a href="lang_analyze.html">ANALYZE</a> command in order to create the statistics
  tables, then copy the precomputed statistics obtained
  from the prototype database into these new statistics tables.
  In that way, statistics from large working data sets can be preloaded
  into newly created application files.
</p>
<a name="crossjoin"></a>
<h3>6.3 Manual Control Of Query Plans Using CROSS JOIN</h3><p>
  Programmers can force SQLite to use a particular loop nesting order
  for a join by using the CROSS JOIN operator instead of just JOIN, 
  INNER JOIN, NATURAL JOIN, or a "," join.  Though CROSS JOINs are
  commutative in theory, SQLite chooses to never reorder the tables in
  a CROSS JOIN.  Hence, the left table of a CROSS JOIN will always be
  in an outer loop relative to the right table.
</p>
<p>
  In the following query, the optimizer is free to reorder the 
  tables of FROM clause anyway it sees fit:
</p>
<blockquote><pre>
  SELECT *
    FROM node AS n1,
         edge AS e,
         node AS n2
   WHERE n1.name = 'alice'
     AND n2.name = 'bob'
     AND e.orig = n1.id
     AND e.dest = n2.id;
</pre></blockquote><p>
  But in the following logically equivalent formulation of the same query,
  the substitution of "CROSS JOIN" for the "," means that the order
  of tables must be N1, E, N2.
</p>
<blockquote><pre>
  SELECT *
    FROM node AS n1 CROSS JOIN
         edge AS e CROSS JOIN
         node AS n2
   WHERE n1.name = 'alice'
     AND n2.name = 'bob'
     AND e.orig = n1.id
     AND e.dest = n2.id;
</pre></blockquote><p>
  In the latter query, the query plan must be 
  <a href="#option2">option 2</a>.  Note that
  you must use the keyword "CROSS" in order to disable the table reordering
  optimization; INNER JOIN, NATURAL JOIN, JOIN, and other similar
  combinations work just like a comma join in that the optimizer is
  free to reorder tables as it sees fit. (Table reordering is also
  disabled on an outer join, but that is because outer joins are not
  associative or commutative. Reordering tables in OUTER JOIN changes
  the result.)
</p>
<p>
  See "<a href="queryplanner-ng.html#fossilcasestudy">The Fossil NGQP Upgrade Case Study</a>" for another real-world example
  of using CROSS JOIN to manually control the nesting order of a join.
  The <a href="queryplanner-ng.html#howtofix">query planner checklist</a> found later in the same document provides
  further guidance on manual control of the query planner.
</p>
<a name="multi_index"></a>
<h2>7.0 Choosing between multiple indices</h2><p>
  Each table in the FROM clause of a query can use at most one index
  (except when the <a href="#or_opt">OR-clause optimization</a> comes into
  play)
  and SQLite strives to use at least one index on each table.  Sometimes,
  two or more indices might be candidates for use on a single table.
  For example:
</p>
<blockquote><pre>
  CREATE TABLE ex2(x,y,z);
  CREATE INDEX ex2i1 ON ex2(x);
  CREATE INDEX ex2i2 ON ex2(y);
  SELECT z FROM ex2 WHERE x=5 AND y=6;
</pre></blockquote><p>
  For the SELECT statement above, the optimizer can use the ex2i1 index
  to lookup rows of ex2 that contain x=5 and then test each row against
  the y=6 term.  Or it can use the ex2i2 index to lookup rows
  of ex2 that contain y=6 then test each of those rows against the
  x=5 term.
</p>
<p>
  When faced with a choice of two or more indices, SQLite tries to estimate
  the total amount of work needed to perform the query using each option.
  It then selects the option that gives the least estimated work.
</p>
<p>
  To help the optimizer get a more accurate estimate of the work involved
  in using various indices, the user may optionally run the <a href="lang_analyze.html">ANALYZE</a> command.
  The <a href="lang_analyze.html">ANALYZE</a> command scans all indices of database where there might
  be a choice between two or more indices and gathers statistics on the
  selectiveness of those indices.  The statistics gathered by
  this scan are stored in special database tables names shows names all
  begin with "<b>sqlite_stat</b>".
  The content of these tables is not updated as the database
  changes so after making significant changes it might be prudent to
  rerun <a href="lang_analyze.html">ANALYZE</a>.
  The results of an ANALYZE command are only available to database connections
  that are opened after the ANALYZE command completes.
</p>
<p>
  The various <b>sqlite_stat</b><i>N</i> tables contain information on how
  selective the various indices are.  For example, the <a href="fileformat2.html#stat1tab">sqlite_stat1</a>
  table might indicate that an equality constraint on column x reduces the
  search space to 10 rows on average, whereas an equality constraint on
  column y reduces the search space to 3 rows on average.  In that case,
  SQLite would prefer to use index ex2i2 since that index is more selective.
</p>
<a name="uplus"></a>
<h3>7.1 Disqualifying WHERE Clause Terms Using Unary-"+"</h3><p>
  Terms of the WHERE clause can be manually disqualified for use with
  indices by prepending a unary <tt><b><big>+</big></b></tt> operator to the column name.  The
  unary <tt><b><big>+</big></b></tt> is a no-op and will not generate any byte code in the prepared
  statement.
  But the unary <tt><b><big>+</big></b></tt> operator will prevent the term from constraining an index.
  So, in the example above, if the query were rewritten as:
</p>
<blockquote><pre>
  SELECT z FROM ex2 WHERE +x=5 AND y=6;
</pre></blockquote><p>
  The <tt><b><big>+</big></b></tt> operator on the <tt><b><big>x</big></b></tt> column will prevent that term from 
  constraining an index.  This would force the use of the ex2i2 index.
</p>
<p>
  Note that the unary <tt><b><big>+</big></b></tt> operator also removes 
  <a href="datatype3.html#affinity">type affinity</a> from
  an expression, and in some cases this can cause subtle changes in
  the meaning of an expression.
  In the example above,
  if column <tt><b><big>x</big></b></tt> has <a href="datatype3.html#affinity">TEXT affinity</a>
  then the comparison "x=5" will be done as text.  But the <tt><b><big>+</big></b></tt> operator
  removes the affinity.  So the comparison "+x=5" will compare the text
  in column <tt><b><big>x</big></b></tt> with the numeric value 5 and will always be false.
</p>
<a name="rangequery"></a>
<h3>7.2 Range Queries</h3><p>
  Consider a slightly different scenario:
</p>
<blockquote><pre>
  CREATE TABLE ex2(x,y,z);
  CREATE INDEX ex2i1 ON ex2(x);
  CREATE INDEX ex2i2 ON ex2(y);
  SELECT z FROM ex2 WHERE x BETWEEN 1 AND 100 AND y BETWEEN 1 AND 100;
</pre></blockquote><p>
  Further suppose that column x contains values spread out
  between 0 and 1,000,000 and column y contains values
  that span between 0 and 1,000.  In that scenario,
  the range constraint on column x should reduce the search space by
  a factor of 10,000 whereas the range constraint on column y should
  reduce the search space by a factor of only 10.  So the ex2i1 index
  should be preferred.
</p>
<p>
  SQLite will make this determination, but only if it has been compiled
  with <a href="compile.html#enable_stat3">SQLITE_ENABLE_STAT3</a> or <a href="compile.html#enable_stat4">SQLITE_ENABLE_STAT4</a>.
  The <a href="compile.html#enable_stat3">SQLITE_ENABLE_STAT3</a> and <a href="compile.html#enable_stat4">SQLITE_ENABLE_STAT4</a> options causes
  the <a href="lang_analyze.html">ANALYZE</a> command to collect a histogram of column content in the
  <a href="fileformat2.html#stat3tab">sqlite_stat3</a> or <a href="fileformat2.html#stat4tab">sqlite_stat4</a> tables and to use this histogram to 
  make a better guess at the best query to use for range constraints
  such as the above.  The main difference between STAT3 and STAT4 is
  that STAT3 records histogram data for only the left-most column of
  an index whereas STAT4 records histogram data for all columns of an
  index.  For single-column indexes, STAT3 and STAT4 work the same.
</p>
<p>
  The histogram data is only useful if the right-hand side of the constraint
  is a simple compile-time constant or <a href="lang_expr.html#varparam">parameter</a> and not an expression.
</p>
<p>
  Another limitation of the histogram data is that it only applies to the
  left-most column on an index.  Consider this scenario:
</p>
<blockquote><pre>
  CREATE TABLE ex3(w,x,y,z);
  CREATE INDEX ex3i1 ON ex2(w, x);
  CREATE INDEX ex3i2 ON ex2(w, y);
  SELECT z FROM ex3 WHERE w=5 AND x BETWEEN 1 AND 100 AND y BETWEEN 1 AND 100;
</pre></blockquote><p>
  Here the inequalities are on columns x and y which are not the
  left-most index columns.  Hence, the histogram data which is collected no
  left-most column of indices is useless in helping to choose between the
  range constraints on columns x and y.
</p>
<h2>8.0 Covering Indices</h2><p>
  When doing an indexed lookup of a row, the usual procedure is to
  do a binary search on the index to find the index entry, then extract
  the <a href="lang_createtable.html#rowid">rowid</a> from the index and use that <a href="lang_createtable.html#rowid">rowid</a> to do a binary search on
  the original table.  Thus a typical indexed lookup involves two
  binary searches.
  If, however, all columns that were to be fetched from the table are
  already available in the index itself, SQLite will use the values
  contained in the index and will never look up the original table
  row.  This saves one binary search for each row and can make many
  queries run twice as fast.
</p>
<p>
  When an index contains all of the data needed for a query and when the
  original table never needs to be consulted, we call that index a
  "covering index".
</p>
<a name="order_by"></a>
<h2>9.0 ORDER BY optimizations</h2><p>
  SQLite attempts to use an index to satisfy the ORDER BY clause of a
  query when possible.
  When faced with the choice of using an index to satisfy WHERE clause
  constraints or satisfying an ORDER BY clause, SQLite does the same
  cost analysis described above
  and chooses the index that it believes will result in the fastest answer.
</p>
<p>
  SQLite will also attempt to use indices to help satisfy GROUP BY clauses
  and the DISTINCT keyword.  If the nested loops of the join can be arranged
  such that rows that are equivalent for the GROUP BY or for the DISTINCT are
  consecutive, then the GROUP BY or DISTINCT logic can determine if the 
  current row is part of the same group or if the current row is distinct
  simply by comparing the current row to the previous row.
  This can be much faster than the alternative of comparing each row to
  all prior rows.
</p>
<a name="partsort"></a>
<h3>9.1 Partial ORDER BY Via Index</h3><p>
  If a query contains an ORDER BY clause with multiple terms, it might
  be that SQLite can use indices to cause rows to come out in the order
  of some prefix of the terms in the ORDER BY but that later terms in
  the ORDER BY are not satisfied.  In that case, SQLite does block sorting.
  Suppose the ORDER BY clause has four terms and the natural order of the
  query results in rows appearing in order of the first two terms.  As
  each row is output by the query engine and enters the sorter, the 
  outputs in the current row corresponding to the first two terms of 
  the ORDER BY are compared against the previous row.  If they have
  changed, the current sort is finished and output and a new sort is
  started.  This results in a slightly faster sort.  But the bigger
  advantages are that many fewer rows need to be held in memory,
  reducing memory requirements, and outputs can begin to appear before
  the core query has run to completion.
</p>
<a name="flattening"></a>
<h2>10.0 Subquery flattening</h2><p>
  When a subquery occurs in the FROM clause of a SELECT, the simplest
  behavior is to evaluate the subquery into a transient table, then run
  the outer SELECT against the transient table.  But such a plan
  can be suboptimal since the transient table will not have any indices
  and the outer query (which is likely a join) will be forced to do a
  full table scan on the transient table.
</p>
<p>
  To overcome this problem, SQLite attempts to flatten subqueries in
  the FROM clause of a SELECT.
  This involves inserting the FROM clause of the subquery into the
  FROM clause of the outer query and rewriting expressions in
  the outer query that refer to the result set of the subquery.
  For example:
</p>
<blockquote><pre>
  SELECT a FROM (SELECT x+y AS a FROM t1 WHERE z<100) WHERE a>5
</pre></blockquote><p>
  Would be rewritten using query flattening as:
</p>
<blockquote><pre>
  SELECT x+y AS a FROM t1 WHERE z<100 AND a>5
</pre></blockquote><p>
  There is a long list of conditions that must all be met in order for
  query flattening to occur.  Some of the constraints are marked as 
  obsolete by italic text.  These extra constraints are retained in the
  documentation to preserve the numbering of the other constraints.
</p>
<p>
  <ol>
  <li value="1">  The subquery and the outer query do not both use aggregates.

  <li value="2">
  The subquery is not an aggregate or the outer query is not a join.

  <li value="3">
  The subquery is not the right operand of a left outer join.

  <li value="4">  The subquery is not DISTINCT.

  <li value="5"> <i>(Subsumed into constraint 4)</i>

  <li value="6">
        The subquery does not use aggregates or the outer query is not
        DISTINCT.

  <li value="7">
  The subquery has a FROM clause.

  <li value="8">
  The subquery does not use LIMIT or the outer query is not a join.

  <li value="9">
  The subquery does not use LIMIT or the outer query does not use
  aggregates.

  <li value="10">
  The subquery does not use aggregates or the outer query does not
  use LIMIT.

  <li value="11">
  The subquery and the outer query do not both have ORDER BY clauses.

  <li value="12"> <i>(Subsumed into constraint 3)</i>

  <li value="13">  The subquery and outer query do not both use LIMIT.

  <li value="14">  The subquery does not use OFFSET.

  <li value="15">
  The outer query is not part of a compound select or the
  subquery does not have a LIMIT clause.

  <li value="16">
  The outer query is not an aggregate or the subquery does
  not contain ORDER BY. 

  <li value="17">
  The sub-query is not a compound select, or it is a UNION ALL 
  compound clause made up entirely of non-aggregate queries, and 
  the parent query:

  <ul>
  <li> is not itself part of a compound select,
  <li> is not an aggregate or DISTINCT query, and
  <li> is not a join.
  </ul>

  The parent and sub-query may contain WHERE clauses. Subject to
  rules (11), (12) and (13), they may also contain ORDER BY,
  LIMIT and OFFSET clauses.

  <li value="18">
  If the sub-query is a compound select, then all terms of the
  ORDER by clause of the parent must be simple references to 
  columns of the sub-query.

  <li value="19">
  The subquery does not use LIMIT or the outer query does not
  have a WHERE clause.

  <li value="20">
  If the sub-query is a compound select, then it must not use
  an ORDER BY clause.

  <li value="21">
  The subquery does not use LIMIT or the outer query is not
  DISTINCT.

  <li value="22"> The subquery is not a recursive CTE.

  <li value="23"> The parent is not a recursive CTE, or the sub-query
  is not a compound query.
  </ol>
</p>
<p>
  The casual reader is not expected to understand or remember any part of
  the list above.  The point of this list is to demonstrate
  that the decision of whether or not to flatten a query is complex.
  
</p>
<p>
  Query flattening is an important optimization when views are used as
  each use of a view is translated into a subquery.
</p>
<a name="minmax"></a>
<h2>11.0 The MIN/MAX optimization</h2><p>
  Queries that contain a single MIN() or MAX() aggregate function whose
  argument is the left-most column of an index might be satisfied
  by doing a single index lookup rather than by scanning the entire table.
  Examples:
</p>
<blockquote><pre>
  SELECT MIN(x) FROM table;
  SELECT MAX(x)+1 FROM table;
</pre></blockquote><a name="autoindex"></a>
<h2>12.0 Automatic Indices</h2><p>
  When no indices are available to aid the evaluation of a query, SQLite
  might create an automatic index that lasts only for the duration
  of a single SQL statement.
  Since the cost of constructing the automatic index is
  O(NlogN) (where N is the number of entries in the table) and the cost of
  doing a full table scan is only O(N), an automatic index will
  only be created if SQLite expects that the lookup will be run more than
  logN times during the course of the SQL statement. Consider an example:
</p>
<blockquote><pre>
  CREATE TABLE t1(a,b);
  CREATE TABLE t2(c,d);
  -- Insert many rows into both t1 and t2
  SELECT * FROM t1, t2 WHERE a=c;
</pre></blockquote><p>
  In the query above, if both t1 and t2 have approximately N rows, then
  without any indices the query will require O(N*N) time.  On the other
  hand, creating an index on table t2 requires O(NlogN) time and then using 
  that index to evaluate the query requires an additional O(NlogN) time.
  In the absence of <a href="lang_analyze.html">ANALYZE</a> information, SQLite guesses that N is one
  million and hence it believes that constructing the automatic index will
  be the cheaper approach.
</p>
<p>
  An automatic index might also be used for a subquery:
</p>
<blockquote><pre>
  CREATE TABLE t1(a,b);
  CREATE TABLE t2(c,d);
  -- Insert many rows into both t1 and t2
  SELECT a, (SELECT d FROM t2 WHERE c=b) FROM t1;
</pre></blockquote><p>
  In this example, the t2 table is used in a subquery to translate values
  of the t1.b column.  If each table contains N rows, SQLite expects that
  the subquery will run N times, and hence it will believe it is faster
  to construct an automatic, transient index on t2 first and then using
  that index to satisfy the N instances of the subquery.
</p>
<p>
  The automatic indexing capability can be disabled at run-time using
  the <a href="pragma.html#pragma_automatic_index">automatic_index pragma</a>.  Automatic indexing is turned on by
  default, but this can be changed so that automatic indexing is off
  by default using the <a href="compile.html#default_automatic_index">SQLITE_DEFAULT_AUTOMATIC_INDEX</a> compile-time option.
  The ability to create automatic indices can be completely disabled by
  compiling with the <a href="compile.html#omit_automatic_index">SQLITE_OMIT_AUTOMATIC_INDEX</a> compile-time option.
</p>
<p>
  In SQLite version 3.8.0, an <a href="rescode.html#warning_autoindex">SQLITE_WARNING_AUTOINDEX</a> message is sent
  to the <a href="errlog.html">error log</a> every time a statement is prepared that uses an
  automatic index.  Application developers can and should use these warnings
  to identify the need for new persistent indices in the schema.
</p>
<p>
  Future releases of SQLite may disable automatic indices by default.
</p>