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Added a long section about proper use of the optimizer-hint

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clauses in CREATE OPERATOR.  Needs markup work.
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Tom Lane 1999-05-21 00:38:33 +00:00
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@ -4,17 +4,32 @@
<Para>
<ProductName>Postgres</ProductName> supports left unary,
right unary and binary
operators. Operators can be overloaded, or re-used
with different numbers and types of arguments. If
operators. Operators can be overloaded; that is,
the same operator name can be used for different operators
that have different numbers and types of arguments. If
there is an ambiguous situation and the system cannot
determine the correct operator to use, it will return
an error and you may have to typecast the left and/or
an error. You may have to typecast the left and/or
right operands to help it understand which operator you
meant to use.
To create an operator for adding two complex numbers
can be done as follows. First we need to create a
function to add the new types. Then, we can create the
operator with the function.
</Para>
<Para>
Every operator is "syntactic sugar" for a call to an
underlying function that does the real work; so you must
first create the underlying function before you can create
the operator. However, an operator is <emphasis>not</emphasis>
merely syntactic sugar, because it carries additional information
that helps the query planner optimize queries that use the
operator. Much of this chapter will be devoted to explaining
that additional information.
</Para>
<Para>
Here is an example of creating an operator for adding two
complex numbers. We assume we've already created the definition
of type complex. First we need a function that does the work;
then we can define the operator:
<ProgramListing>
CREATE FUNCTION complex_add(complex, complex)
@ -32,11 +47,7 @@ CREATE OPERATOR + (
</Para>
<Para>
We've shown how to create a binary operator here. To
create unary operators, just omit one of leftarg (for
left unary) or rightarg (for right unary).
If we give the system enough type information, it can
automatically figure out which operators to use.
Now we can do:
<ProgramListing>
SELECT (a + b) AS c FROM test_complex;
@ -51,8 +62,18 @@ SELECT (a + b) AS c FROM test_complex;
</ProgramListing>
</Para>
<Para>
We've shown how to create a binary operator here. To
create unary operators, just omit one of leftarg (for
left unary) or rightarg (for right unary). The procedure
clause and the argument clauses are the only required items
in CREATE OPERATOR. The COMMUTATOR clause shown in the example
is an optional hint to the query optimizer. Further details about
COMMUTATOR and other optimizer hints appear below.
</Para>
<sect1>
<title>Hash Join Operators</title>
<title>Operator Optimization Information</title>
<note>
<title>Author</title>
@ -62,39 +83,335 @@ SELECT (a + b) AS c FROM test_complex;
</note>
<para>
The assumption underlying hash join is that two values that will be
considered equal by the comparison operator will always have the same
hash value. If two values get put in different hash buckets, the join
will never compare them at all, so they are necessarily treated as
unequal.
A <ProductName>Postgres</ProductName> operator definition can include
several optional clauses that tell the system useful things about how
the operator behaves. These clauses should be provided whenever
appropriate, because they can make for considerable speedups in execution
of queries that use the operator. But if you provide them, you must be
sure that they are right! Incorrect use of an optimization clause can
result in backend crashes, subtly wrong output, or other Bad Things.
You can always leave out an optimization clause if you are not sure
about it --- the only consequence is that queries might run slower than
they need to.
</para>
<para>
But we have a number of datatypes for which the "=" operator is not
a straight bitwise comparison. For example, intervaleq is not bitwise
at all; it considers two time intervals equal if they have the same
Additional optimization clauses might be added in future versions of
<ProductName>Postgres</ProductName>. The ones described here are all
the ones that release 6.5 understands.
</para>
<sect2>
<title>COMMUTATOR</title>
<para>
The COMMUTATOR clause, if provided, names an operator that is the
commutator of the operator being defined. We say that operator A is the
commutator of operator B if (x A y) equals (y B x) for all possible input
values x,y. Notice that B is also the commutator of A. For example,
operators '<' and '>' for a particular datatype are usually each others'
commutators, and operator '+' is usually commutative with itself.
But operator '-' is usually not commutative with anything.
</para>
<para>
The left argument type of a commuted operator is the same as the
right argument type of its commutator, and vice versa. So the name of
the commutator operator is all that <ProductName>Postgres</ProductName>
needs to be given to look up the commutator, and that's all that need
be provided in the COMMUTATOR clause.
</para>
<para>
When you are defining a self-commutative operator, you just do it.
When you are defining a pair of commutative operators, things are
a little trickier: how can the first one to be defined refer to the
other one, which you haven't defined yet? There are two solutions
to this problem:
</para>
<para>
One way is to omit the COMMUTATOR clause in the first operator that
you define, and then provide one in the second operator's definition.
Since <ProductName>Postgres</ProductName> knows that commutative
operators come in pairs, when it sees the second definition it will
automatically go back and fill in the missing COMMUTATOR clause in
the first definition.
</para>
<para>
The other, more straightforward way is just to include COMMUTATOR clauses
in both definitions. When <ProductName>Postgres</ProductName> processes
the first definition and realizes that COMMUTATOR refers to a non-existent
operator, the system will make a dummy entry for that operator in the
system's pg_operator table. This dummy entry will have valid data only
for the operator name, left and right argument types, and result type,
since that's all that <ProductName>Postgres</ProductName> can deduce
at this point. The first operator's catalog entry will link to this
dummy entry. Later, when you define the second operator, the system
updates the dummy entry with the additional information from the second
definition. If you try to use the dummy operator before it's been filled
in, you'll just get an error message. (Note: this procedure did not work
reliably in <ProductName>Postgres</ProductName> versions before 6.5,
but it is now the recommended way to do things.)
</para>
</sect2>
<sect2>
<title>NEGATOR</title>
<para>
The NEGATOR clause, if provided, names an operator that is the
negator of the operator being defined. We say that operator A
is the negator of operator B if both return boolean results and
(x A y) equals NOT (x B y) for all possible inputs x,y.
Notice that B is also the negator of A.
For example, '<' and '>=' are a negator pair for most datatypes.
An operator can never be validly be its own negator.
</para>
<para>
Unlike COMMUTATOR, a pair of unary operators could validly be marked
as each others' negators; that would mean (A x) equals NOT (B x)
for all x, or the equivalent for right-unary operators.
</para>
<para>
An operator's negator must have the same left and/or right argument types
as the operator itself, so just as with COMMUTATOR, only the operator
name need be given in the NEGATOR clause.
</para>
<para>
Providing NEGATOR is very helpful to the query optimizer since
it allows expressions like NOT (x = y) to be simplified into
x <> y. This comes up more often than you might think, because
NOTs can be inserted as a consequence of other rearrangements.
</para>
<para>
Pairs of negator operators can be defined using the same methods
explained above for commutator pairs.
</para>
</sect2>
<sect2>
<title>RESTRICT</title>
<para>
The RESTRICT clause, if provided, names a restriction selectivity
estimation function for the operator (note that this is a function
name, not an operator name). RESTRICT clauses only make sense for
binary operators that return boolean. The idea behind a restriction
selectivity estimator is to guess what fraction of the rows in a
table will satisfy a WHERE-clause condition of the form
<ProgramListing>
field OP constant
</ProgramListing>
for the current operator and a particular constant value.
This assists the optimizer by
giving it some idea of how many rows will be eliminated by WHERE
clauses that have this form. (What happens if the constant is on
the left, you may be wondering? Well, that's one of the things that
COMMUTATOR is for...)
</para>
<para>
Writing new restriction selectivity estimation functions is far beyond
the scope of this chapter, but fortunately you can usually just use
one of the system's standard estimators for many of your own operators.
These are the standard restriction estimators:
<ProgramListing>
eqsel for =
neqsel for <>
intltsel for < or <=
intgtsel for > or >=
</ProgramListing>
It might seem a little odd that these are the categories, but they
make sense if you think about it. '=' will typically accept only
a small fraction of the rows in a table; '<>' will typically reject
only a small fraction. '<' will accept a fraction that depends on
where the given constant falls in the range of values for that table
column (which, it just so happens, is information collected by
VACUUM ANALYZE and made available to the selectivity estimator).
'<=' will accept a slightly larger fraction than '<' for the same
comparison constant, but they're close enough to not be worth
distinguishing, especially since we're not likely to do better than a
rough guess anyhow. Similar remarks apply to '>' and '>='.
</para>
<para>
You can frequently get away with using either eqsel or neqsel for
operators that have very high or very low selectivity, even if they
aren't really equality or inequality. For example, the regular expression
matching operators (~, ~*, etc) use eqsel on the assumption that they'll
usually only match a small fraction of the entries in a table.
</para>
<sect2>
<title>JOIN</title>
<para>
The JOIN clause, if provided, names a join selectivity
estimation function for the operator (note that this is a function
name, not an operator name). JOIN clauses only make sense for
binary operators that return boolean. The idea behind a join
selectivity estimator is to guess what fraction of the rows in a
pair of tables will satisfy a WHERE-clause condition of the form
<ProgramListing>
table1.field1 OP table2.field2
</ProgramListing>
for the current operator. As with the RESTRICT clause, this helps
the optimizer very substantially by letting it figure out which
of several possible join sequences is likely to take the least work.
</para>
<para>
As before, this chapter will make no attempt to explain how to write
a join selectivity estimator function, but will just suggest that
you use one of the standard estimators if one is applicable:
<ProgramListing>
eqjoinsel for =
neqjoinsel for <>
intltjoinsel for < or <=
intgtjoinsel for > or >=
</ProgramListing>
</para>
</sect2>
<sect2>
<title>HASHES</title>
<para>
The HASHES clause, if present, tells the system that it is OK to
use the hash join method for a join based on this operator. HASHES
only makes sense for binary operators that return boolean --- and
in practice, the operator had better be equality for some data type.
</para>
<para>
The assumption underlying hash join is that the join operator can
only return TRUE for pairs of left and right values that hash to the
same hash code. If two values get put in different hash buckets, the
join will never compare them at all, implicitly assuming that the
result of the join operator must be FALSE. So it never makes sense
to specify HASHES for operators that do not represent equality.
</para>
<para>
In fact, logical equality is not good enough either --- the operator
had better represent pure bitwise equality, because the hash function
will be computed on the memory representation of the values regardless
of what the bits mean. For example, equality of
time intervals is not bitwise equality; the interval equality operator
considers two time intervals equal if they have the same
duration, whether or not their endpoints are identical. What this means
is that a join using "=" between interval fields will yield different
is that a join using "=" between interval fields would yield different
results if implemented as a hash join than if implemented another way,
because a large fraction of the pairs that should match will hash to
different values and will never be compared.
different values and will never be compared by the hash join. But
if the optimizer chose to use a different kind of join, all the pairs
that the equality operator says are equal will be found.
We don't want that kind of inconsistency, so we don't mark interval
equality as hashable.
</para>
<para>
I believe the same problem exists for float data; for example, on
IEEE-compliant machines, minus zero and plus zero have different bit
patterns (hence different hash values) but should be considered equal.
A hashjoin will get it wrong.
There are also machine-dependent ways in which a hash join might fail
to do the right thing. For example, if your datatype
is a structure in which there may be uninteresting pad bits, it's unsafe
to mark the equality operator HASHES. (Unless, perhaps, you write
your other operators to ensure that the unused bits are always zero.)
Another example is that the FLOAT datatypes are unsafe for hash
joins. On machines that meet the IEEE floating point standard, minus
zero and plus zero are different values (different bit patterns) but
they are defined to compare equal. So, if float equality were marked
HASHES, a minus zero and a plus zero would probably not be matched up
by a hash join, but they would be matched up by any other join process.
</para>
<para>
I will go through pg_operator and remove the hashable flag from
operators that are not safely hashable, but I see no way to
automatically check for this sort of mistake. The only long-term
answer is to raise the consciousness of datatype creators about what
it means to set the oprcanhash flag. Don't do it unless your equality
operator can be implemented as memcmp()!
The bottom line is that you should probably only use HASHES for
equality operators that are (or could be) implemented by memcmp().
</para>
</sect2>
<sect2>
<title>SORT1 and SORT2</title>
<para>
The SORT clauses, if present, tell the system that it is OK to use
the merge join method for a join based on the current operator.
Both must be specified if either is. The current operator must be
equality for some pair of data types, and the SORT1 and SORT2 clauses
name the ordering operator ('<' operator) for the left and right-side
data types respectively.
</para>
<para>
Merge join is based on the idea of sorting the left and righthand tables
into order and then scanning them in parallel. So, both data types must
be capable of being fully ordered, and the join operator must be one
that can only succeed for pairs of values that fall at the "same place"
in the sort order. In practice this means that the join operator must
behave like equality. But unlike hashjoin, where the left and right
data types had better be the same (or at least bitwise equivalent),
it is possible to mergejoin two
distinct data types so long as they are logically compatible. For
example, the int2-versus-int4 equality operator is mergejoinable.
We only need sorting operators that will bring both datatypes into a
logically compatible sequence.
</para>
<para>
When specifying merge sort operators, the current operator and both
referenced operators must return boolean; the SORT1 operator must have
both input datatypes equal to the current operator's left argument type,
and the SORT2 operator must have
both input datatypes equal to the current operator's right argument type.
(As with COMMUTATOR and NEGATOR, this means that the operator name is
sufficient to specify the operator, and the system is able to make dummy
operator entries if you happen to define the equality operator before
the other ones.)
</para>
<para>
In practice you should only write SORT clauses for an '=' operator,
and the two referenced operators should always be named '<'. Trying
to use merge join with operators named anything else will result in
hopeless confusion, for reasons we'll see in a moment.
</para>
<para>
There are additional restrictions on operators that you mark
mergejoinable. These restrictions are not currently checked by
CREATE OPERATOR, but a merge join may fail at runtime if any are
not true:
</para>
<para>
The mergejoinable equality operator must have a commutator
(itself if the two data types are the same, or a related equality operator
if they are different).
</para>
<para>
There must be '<' and '>' ordering operators having the same left and
right input datatypes as the mergejoinable operator itself. These
operators <emphasis>must</emphasis> be named '<' and '>' --- you do
not have any choice in the matter, since there is no provision for
specifying them explicitly. Note that if the left and right data types
are different, neither of these operators is the same as either
SORT operator. But they had better order the data values compatibly
with the SORT operators, or mergejoin will fail to work.
</para>
</sect2>
</sect1>
</Chapter>