optimizer

Summary
-------

These directories take the Query structure returned by the parser, and
generate a plan used by the executor.  The /plan directory generates the
actual output plan, the /path code generates all possible ways to join the
tables, and /prep handles various preprocessing steps for special cases.
/util is utility stuff.  /geqo is the separate "genetic optimization" planner
--- it does a semi-random search through the join tree space, rather than
exhaustively considering all possible join trees.  (But each join considered
by /geqo is given to /path to create paths for, so we consider all possible
implementation paths for each specific join pair even in GEQO mode.)


Paths and Join Pairs
--------------------

During the planning/optimizing process, we build "Path" trees representing
the different ways of doing a query.  We select the cheapest Path that
generates the desired relation and turn it into a Plan to pass to the
executor.  (There is pretty much a one-to-one correspondence between the
Path and Plan trees, but Path nodes omit info that won't be needed during
planning, and include info needed for planning that won't be needed by the
executor.)

The optimizer builds a RelOptInfo structure for each base relation used in
the query.  Base rels are either primitive tables, or subquery subselects
that are planned via a separate recursive invocation of the planner.  A
RelOptInfo is also built for each join relation that is considered during
planning.  A join rel is simply a combination of base rels.  There is only
one join RelOptInfo for any given set of baserels --- for example, the join
{A B C} is represented by the same RelOptInfo no matter whether we build it
by joining A and B first and then adding C, or joining B and C first and
then adding A, etc.  These different means of building the joinrel are
represented as Paths.  For each RelOptInfo we build a list of Paths that
represent plausible ways to implement the scan or join of that relation.
Once we've considered all the plausible Paths for a rel, we select the one
that is cheapest according to the planner's cost estimates.  The final plan
is derived from the cheapest Path for the RelOptInfo that includes all the
base rels of the query.

Possible Paths for a primitive table relation include plain old sequential
scan, plus index scans for any indexes that exist on the table.  A subquery
base relation just has one Path, a "SubqueryScan" path (which links to the
subplan that was built by a recursive invocation of the planner).

Joins always occur using two RelOptInfos.  One is outer, the other inner.
Outers drive lookups of values in the inner.  In a nested loop, lookups of
values in the inner occur by scanning the inner path once per outer tuple
to find each matching inner row.  In a mergejoin, inner and outer rows are
ordered, and are accessed in order, so only one scan is required to perform
the entire join: both inner and outer paths are scanned in-sync.  (There's
not a lot of difference between inner and outer in a mergejoin...)  In a
hashjoin, the inner is scanned first and all its rows are entered in a
hashtable, then the outer is scanned and for each row we lookup the join
key in the hashtable.

A Path for a join relation is actually a tree structure, with the top
Path node representing the join method.  It has left and right subpaths
that represent the scan or join methods used for the two input relations.


Join Tree Construction
----------------------

The optimizer generates optimal query plans by doing a more-or-less
exhaustive search through the ways of executing the query.  The best Path
tree is found by a recursive process:

1) Take each base relation in the query, and make a RelOptInfo structure
for it.  Find each potentially useful way of accessing the relation,
including sequential and index scans, and make a Path representing that
way.  All the Paths made for a given relation are placed in its
RelOptInfo.pathlist.  (Actually, we discard Paths that are obviously
inferior alternatives before they ever get into the pathlist --- what
ends up in the pathlist is the cheapest way of generating each potentially
useful sort ordering of the relation.)  Also create RelOptInfo.joininfo
nodes that list all the join clauses that involve this relation.  For
example, the WHERE clause "tab1.col1 = tab2.col1" generates a JoinInfo
for tab1 listing tab2 as an unjoined relation, and also one for tab2
showing tab1 as an unjoined relation.

If we have only a single base relation in the query, we are done.
Otherwise we have to figure out how to join the base relations into a
single join relation.

2) If the query's FROM clause contains explicit JOIN clauses, we join
those pairs of relations in exactly the tree structure indicated by the
JOIN clauses.  (This is absolutely necessary when dealing with outer JOINs.
For inner JOINs we have more flexibility in theory, but don't currently
exploit it in practice.)  For each such join pair, we generate a Path
for each feasible join method, and select the cheapest Path.  Note that
the JOIN clause structure determines the join Path structure, but it
doesn't constrain the join implementation method at each join (nestloop,
merge, hash), nor does it say which rel is considered outer or inner at
each join.  We consider all these possibilities in building Paths.

3) At the top level of the FROM clause we will have a list of relations
that are either base rels or joinrels constructed per JOIN directives.
We can join these rels together in any order the planner sees fit.
The standard (non-GEQO) planner does this as follows:

Consider joining each RelOptInfo to each other RelOptInfo specified in its
RelOptInfo.joininfo, and generate a Path for each possible join method for
each such pair.  (If we have a RelOptInfo with no join clauses, we have no
choice but to generate a clauseless Cartesian-product join; so we consider
joining that rel to each other available rel.  But in the presence of join
clauses we will only consider joins that use available join clauses.)

If we only had two relations in the FROM list, we are done: we just pick
the cheapest path for the join RelOptInfo.  If we had more than two, we now
need to consider ways of joining join RelOptInfos to each other to make
join RelOptInfos that represent more than two FROM items.

The join tree is constructed using a "dynamic programming" algorithm:
in the first pass (already described) we consider ways to create join rels
representing exactly two FROM items.  The second pass considers ways
to make join rels that represent exactly three FROM items; the next pass,
four items, etc.  The last pass considers how to make the final join
relation that includes all FROM items --- obviously there can be only one
join rel at this top level, whereas there can be more than one join rel
at lower levels.  At each level we use joins that follow available join
clauses, if possible, just as described for the first level.

For example:

    SELECT  *
    FROM    tab1, tab2, tab3, tab4
    WHERE   tab1.col = tab2.col AND
        tab2.col = tab3.col AND
        tab3.col = tab4.col

    Tables 1, 2, 3, and 4 are joined as:
    {1 2},{2 3},{3 4}
    {1 2 3},{2 3 4}
    {1 2 3 4}
    (other possibilities will be excluded for lack of join clauses)

    SELECT  *
    FROM    tab1, tab2, tab3, tab4
    WHERE   tab1.col = tab2.col AND
        tab1.col = tab3.col AND
        tab1.col = tab4.col

    Tables 1, 2, 3, and 4 are joined as:
    {1 2},{1 3},{1 4}
    {1 2 3},{1 3 4},{1 2 4}
    {1 2 3 4}

We consider left-handed plans (the outer rel of an upper join is a joinrel,
but the inner is always a single FROM item); right-handed plans (outer rel
is always a single item); and bushy plans (both inner and outer can be
joins themselves).  For example, when building {1 2 3 4} we consider
joining {1 2 3} to {4} (left-handed), {4} to {1 2 3} (right-handed), and
{1 2} to {3 4} (bushy), among other choices.  Although the jointree
scanning code produces these potential join combinations one at a time,
all the ways to produce the same set of joined base rels will share the
same RelOptInfo, so the paths produced from different join combinations
that produce equivalent joinrels will compete in add_path.

Once we have built the final join rel, we use either the cheapest path
for it or the cheapest path with the desired ordering (if that's cheaper
than applying a sort to the cheapest other path).


Pulling up subqueries
---------------------

As we described above, a subquery appearing in the range table is planned
independently and treated as a "black box" during planning of the outer
query.  This is necessary when the subquery uses features such as
aggregates, GROUP, or DISTINCT.  But if the subquery is just a simple
scan or join, treating the subquery as a black box may produce a poor plan
compared to considering it as part of the entire plan search space.
Therefore, at the start of the planning process the planner looks for
simple subqueries and pulls them up into the main query's jointree.

Pulling up a subquery may result in FROM-list joins appearing below the top
of the join tree.  Each FROM-list is planned using the dynamic-programming
search method described above.

If pulling up a subquery produces a FROM-list as a direct child of another
FROM-list (with no explicit JOIN directives between), then we can merge the
two FROM-lists together.  Once that's done, the subquery is an absolutely
integral part of the outer query and will not constrain the join tree
search space at all.  However, that could result in unpleasant growth of
planning time, since the dynamic-programming search has runtime exponential
in the number of FROM-items considered.  Therefore, we don't merge
FROM-lists if the result would have too many FROM-items in one list.


Optimizer Functions
-------------------

The primary entry point is planner().

planner()
 set up for recursive handling of subqueries
 do final cleanup after planning.
-subquery_planner()
 pull up subqueries from rangetable, if possible
 simplify constant expressions
 canonicalize qual
     Attempt to reduce WHERE clause to either CNF or DNF canonical form.
     CNF (top-level-AND) is preferred, since the optimizer can then use
     any of the AND subclauses to filter tuples; but quals that are in
     or close to DNF form will suffer exponential expansion if we try to
     force them to CNF.  In pathological cases either transform may expand
     the qual unreasonably; so we may have to leave it un-normalized,
     thereby reducing the accuracy of selectivity estimates.
 process sublinks
 convert Vars of outer query levels into Params
--grouping_planner()
  preprocess target list for non-SELECT queries
  handle UNION/INTERSECT/EXCEPT, GROUP BY, HAVING, aggregates,
	ORDER BY, DISTINCT, LIMIT
--query_planner()
   pull out constant quals, which can be used to gate execution of the
	whole plan (if any are found, we make a top-level Result node
	to do the gating)
   make a simplified target list that only contains Vars, no expressions
---subplanner()
    make list of base relations used in query
    split up the qual into restrictions (a=1) and joins (b=c)
    find qual clauses that enable merge and hash joins
----make_one_rel()
     set_base_rel_pathlist()
      find scan and all index paths for each base relation
      find selectivity of columns used in joins
-----make_one_rel_by_joins()
      jump to geqo if needed
      else call make_rels_by_joins() for each level of join tree needed
      make_rels_by_joins():
        For each joinrel of the prior level, do make_rels_by_clause_joins()
        if it has join clauses, or make_rels_by_clauseless_joins() if not.
        Also generate "bushy plan" joins between joinrels of lower levels.
      Back at make_one_rel_by_joins(), apply set_cheapest() to extract the
      cheapest path for each newly constructed joinrel.
      Loop back if this wasn't the top join level.
   Back at query_planner:
   put back constant quals and non-simplified target list
 Back at grouping_planner:
 do grouping(GROUP)
 do aggregates
 make unique(DISTINCT)
 make sort(ORDER BY)
 make limit(LIMIT/OFFSET)


Optimizer Data Structures
-------------------------

RelOptInfo      - a relation or joined relations

 RestrictInfo   - restriction clauses, like "x = 3"
 JoinInfo       - join clauses, including the relids needed for the join

 Path           - every way to generate a RelOptInfo(sequential,index,joins)
  SeqScan       - a plain Path node with nodeTag = T_SeqScan
  IndexPath     - index scans
  NestPath      - nested-loop joins
  MergePath     - merge joins
  HashPath      - hash joins

 PathKeys       - a data structure representing the ordering of a path

The optimizer spends a good deal of its time worrying about the ordering
of the tuples returned by a path.  The reason this is useful is that by
knowing the sort ordering of a path, we may be able to use that path as
the left or right input of a mergejoin and avoid an explicit sort step.
Nestloops and hash joins don't really care what the order of their inputs
is, but mergejoin needs suitably ordered inputs.  Therefore, all paths
generated during the optimization process are marked with their sort order
(to the extent that it is known) for possible use by a higher-level merge.

It is also possible to avoid an explicit sort step to implement a user's
ORDER BY clause if the final path has the right ordering already, so the
sort ordering is of interest even at the top level.  subplanner() will
look for the cheapest path with a sort order matching the desired order,
and will compare its cost to the cost of using the cheapest-overall path
and doing an explicit sort.

When we are generating paths for a particular RelOptInfo, we discard a path
if it is more expensive than another known path that has the same or better
sort order.  We will never discard a path that is the only known way to
achieve a given sort order (without an explicit sort, that is).  In this
way, the next level up will have the maximum freedom to build mergejoins
without sorting, since it can pick from any of the paths retained for its
inputs.


PathKeys
--------

The PathKeys data structure represents what is known about the sort order
of a particular Path.

Path.pathkeys is a List of Lists of PathKeyItem nodes that represent
the sort order of the result generated by the Path.  The n'th sublist
represents the n'th sort key of the result.

In single/base relation RelOptInfo's, the Paths represent various ways
of scanning the relation and the resulting ordering of the tuples.
Sequential scan Paths have NIL pathkeys, indicating no known ordering.
Index scans have Path.pathkeys that represent the chosen index's ordering,
if any.  A single-key index would create a pathkey with a single sublist,
e.g. ( (tab1.indexkey1/sortop1) ).  A multi-key index generates a sublist
per key, e.g. ( (tab1.indexkey1/sortop1) (tab1.indexkey2/sortop2) ) which
shows major sort by indexkey1 (ordering by sortop1) and minor sort by
indexkey2 with sortop2.

Note that a multi-pass indexscan (OR clause scan) has NIL pathkeys since
we can say nothing about the overall order of its result.  Also, an
indexscan on an unordered type of index generates NIL pathkeys.  However,
we can always create a pathkey by doing an explicit sort.  The pathkeys
for a Sort plan's output just represent the sort key fields and the
ordering operators used.

Things get more interesting when we consider joins.  Suppose we do a
mergejoin between A and B using the mergeclause A.X = B.Y.  The output
of the mergejoin is sorted by X --- but it is also sorted by Y.  We
represent this fact by listing both keys in a single pathkey sublist:
( (A.X/xsortop B.Y/ysortop) ).  This pathkey asserts that the major
sort order of the Path can be taken to be *either* A.X or B.Y.
They are equal, so they are both primary sort keys.  By doing this,
we allow future joins to use either var as a pre-sorted key, so upper
Mergejoins may be able to avoid having to re-sort the Path.  This is
why pathkeys is a List of Lists.

We keep a sortop associated with each PathKeyItem because cross-data-type
mergejoins are possible; for example int4 = int8 is mergejoinable.
In this case we need to remember that the left var is ordered by int4lt
while the right var is ordered by int8lt.  So the different members of
each sublist could have different sortops.

Note that while the order of the top list is meaningful (primary vs.
secondary sort key), the order of each sublist is arbitrary.  Each sublist
should be regarded as a set of equivalent keys, with no significance
to the list order.

With a little further thought, it becomes apparent that pathkeys for
joins need not only come from mergejoins.  For example, if we do a
nestloop join between outer relation A and inner relation B, then any
pathkeys relevant to A are still valid for the join result: we have
not altered the order of the tuples from A.  Even more interesting,
if there was a mergeclause (more formally, an "equijoin clause") A.X=B.Y,
and A.X was a pathkey for the outer relation A, then we can assert that
B.Y is a pathkey for the join result; X was ordered before and still is,
and the joined values of Y are equal to the joined values of X, so Y
must now be ordered too.  This is true even though we used neither an
explicit sort nor a mergejoin on Y.

More generally, whenever we have an equijoin clause A.X = B.Y and a
pathkey A.X, we can add B.Y to that pathkey if B is part of the joined
relation the pathkey is for, *no matter how we formed the join*.  It works
as long as the clause has been applied at some point while forming the
join relation.  (In the current implementation, we always apply qual
clauses as soon as possible, ie, as far down in the plan tree as possible.
So we can treat the pathkeys as equivalent everywhere.  The exception is
when the relations A and B are joined inside the nullable side of an
OUTER JOIN and the equijoin clause comes from above the OUTER JOIN.  In this
case we cannot apply the qual as soon as A and B are joined, so we do not
consider the pathkeys to be equivalent.  This could be improved if we wanted
to go to the trouble of making pathkey equivalence be context-dependent,
but that seems much more complex than it's worth.)

In short, then: when producing the pathkeys for a merge or nestloop join,
we can keep all of the keys of the outer path, since the ordering of the
outer path will be preserved in the result.  Furthermore, we can add to
each pathkey sublist any inner vars that are equijoined to any of the
outer vars in the sublist; this works regardless of whether we are
implementing the join using that equijoin clause as a mergeclause,
or merely enforcing the clause after-the-fact as a qpqual filter.

Although Hashjoins also work only with equijoin operators, it is *not*
safe to consider the output of a Hashjoin to be sorted in any particular
order --- not even the outer path's order.  This is true because the
executor might have to split the join into multiple batches.  Therefore
a Hashjoin is always given NIL pathkeys.  (Also, we need to use only
mergejoinable operators when deducing which inner vars are now sorted,
because a mergejoin operator tells us which left- and right-datatype
sortops can be considered equivalent, whereas a hashjoin operator
doesn't imply anything about sort order.)

Pathkeys are also useful to represent an ordering that we wish to achieve,
since they are easily compared to the pathkeys of a potential candidate
path.  So, SortClause lists are turned into pathkeys lists for use inside
the optimizer.

OK, now for how it *really* works:

We did implement pathkeys just as described above, and found that the
planner spent a huge amount of time comparing pathkeys, because the
representation of pathkeys as unordered lists made it expensive to decide
whether two were equal or not.  So, we've modified the representation
as described next.

If we scan the WHERE clause for equijoin clauses (mergejoinable clauses)
during planner startup, we can construct lists of equivalent pathkey items
for the query.  There could be more than two items per equivalence set;
for example, WHERE A.X = B.Y AND B.Y = C.Z AND D.R = E.S creates the
equivalence sets { A.X B.Y C.Z } and { D.R E.S } (plus associated sortops).
Any pathkey item that belongs to an equivalence set implies that all the
other items in its set apply to the relation too, or at least all the ones
that are for fields present in the relation.  (Some of the items in the
set might be for as-yet-unjoined relations.)  Furthermore, any multi-item
pathkey sublist that appears at any stage of planning the query *must* be
a subset of one or another of these equivalence sets; there's no way we'd
have put two items in the same pathkey sublist unless they were equijoined
in WHERE.

Now suppose that we allow a pathkey sublist to contain pathkey items for
vars that are not yet part of the pathkey's relation.  This introduces
no logical difficulty, because such items can easily be seen to be
irrelevant; we just mandate that they be ignored.  But having allowed
this, we can declare (by fiat) that any multiple-item pathkey sublist
must be "equal()" to the appropriate equivalence set.  In effect,
whenever we make a pathkey sublist that mentions any var appearing in an
equivalence set, we instantly add all the other vars equivalenced to it,
whether they appear yet in the pathkey's relation or not.  And we also
mandate that the pathkey sublist appear in the same order as the
equivalence set it comes from.

In fact, we can go even further, and say that the canonical representation
of a pathkey sublist is a pointer directly to the relevant equivalence set,
which is kept in a list of pathkey equivalence sets for the query.  Then
pathkey sublist comparison reduces to pointer-equality checking!  To do this
we also have to add single-element pathkey sublists to the query's list of
equivalence sets, but that's a small price to pay.

By the way, it's OK and even useful for us to build equivalence sets
that mention multiple vars from the same relation.  For example, if
we have WHERE A.X = A.Y and we are scanning A using an index on X,
we can legitimately conclude that the path is sorted by Y as well;
and this could be handy if Y is the variable used in other join clauses
or ORDER BY.  So, any WHERE clause with a mergejoinable operator can
contribute to an equivalence set, even if it's not a join clause.

As sketched so far, equijoin operators allow us to conclude that
A.X = B.Y and B.Y = C.Z together imply A.X = C.Z, even when different
datatypes are involved.  What is not immediately obvious is that to use
the "canonical pathkey" representation, we *must* make this deduction.
An example (from a real bug in Postgres 7.0) is a mergejoin for a query
like
	SELECT * FROM t1, t2 WHERE t1.f2 = t2.f3 AND t1.f1 = t2.f3;
The canonical-pathkey mechanism is able to deduce that t1.f1 = t1.f2
(ie, both appear in the same canonical pathkey set).  If we sort t1
and then apply a mergejoin, we *must* filter the t1 tuples using the
implied qualification f1 = f2, because otherwise the output of the sort
will be ordered by f1 or f2 (whichever we sort on) but not both.  The
merge will then fail since (depending on which qual clause it applies
first) it's expecting either ORDER BY f1,f2 or ORDER BY f2,f1, but the
actual output of the sort has neither of these orderings.  The best fix
for this is to generate all the implied equality constraints for each
equijoin set and add these clauses to the query's qualification list.
In other words, we *explicitly* deduce f1 = f2 and add this to the WHERE
clause.  The constraint will be applied as a qpqual to the output of the
scan on t1, resulting in sort output that is indeed ordered by both vars.
This approach provides more information to the selectivity estimation
code than it would otherwise have, and reduces the number of tuples
processed in join stages, so it's a win to make these deductions even
if we weren't forced to.

Yet another implication of all this is that mergejoinable operators
must form closed equivalence sets.  For example, if "int2 = int4"
and "int4 = int8" are both marked mergejoinable, then there had better
be a mergejoinable "int2 = int8" operator as well.  Otherwise, when
we're given WHERE int2var = int4var AND int4var = int8var, we'll fail
while trying to create a representation of the implied clause
int2var = int8var.

An additional refinement we can make is to insist that canonical pathkey
lists (sort orderings) do not mention the same pathkey set more than once.
For example, a pathkey list ((A) (B) (A)) is redundant --- the second
occurrence of (A) does not change the ordering, since the data must already
be sorted by A.  Although a user probably wouldn't write ORDER BY A,B,A
directly, such redundancies are more probable once equijoin equivalences
have been considered.  Also, the system is likely to generate redundant
pathkey lists when computing the sort ordering needed for a mergejoin.  By
eliminating the redundancy, we save time and improve planning, since the
planner will more easily recognize equivalent orderings as being equivalent.

-- bjm & tgl