A PostgreSQL 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 slow queries, 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.
Additional optimization clauses might be added in future versions of PostgreSQL. The ones described here are all the ones that release 14.10 understands.
It is also possible to attach a planner support function to the function that underlies an operator, providing another way of telling the system about the behavior of the operator. See Section 38.11 for more information.
COMMUTATOR
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 data type are usually each others'
commutators, and operator +
is usually commutative with itself.
But operator -
is usually not commutative with anything.
The left operand type of a commutable operator is the same as the
right operand type of its commutator, and vice versa. So the name of
the commutator operator is all that PostgreSQL
needs to be given to look up the commutator, and that's all that needs to
be provided in the COMMUTATOR
clause.
It's critical to provide commutator information for operators that
will be used in indexes and join clauses, because this allows the
query optimizer to “flip around” such a clause to the forms
needed for different plan types. For example, consider a query with
a WHERE clause like tab1.x = tab2.y
, where tab1.x
and tab2.y
are of a user-defined type, and suppose that
tab2.y
is indexed. The optimizer cannot generate an
index scan unless it can determine how to flip the clause around to
tab2.y = tab1.x
, because the index-scan machinery expects
to see the indexed column on the left of the operator it is given.
PostgreSQL will not simply
assume that this is a valid transformation — the creator of the
=
operator must specify that it is valid, by marking the
operator with commutator information.
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:
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 PostgreSQL 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.
The other, more straightforward way is just to include COMMUTATOR
clauses
in both definitions. When PostgreSQL processes
the first definition and realizes that COMMUTATOR
refers to a nonexistent
operator, the system will make a dummy entry for that operator in the
system catalog. This dummy entry will have valid data only
for the operator name, left and right operand types, and result type,
since that's all that PostgreSQL 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.
NEGATOR
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 data types.
An operator can never validly be its own negator.
Unlike commutators, a pair of unary operators could validly be marked as each other's negators; that would mean (A x) equals NOT (B x) for all x.
An operator's negator must have the same left and/or right operand types
as the operator to be defined, so just as with COMMUTATOR
, only the operator
name need be given in the NEGATOR
clause.
Providing a 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
NOT
operations can be inserted as a consequence of other rearrangements.
Pairs of negator operators can be defined using the same methods explained above for commutator pairs.
RESTRICT
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:
column OP constant
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 might be wondering? Well, that's one of the things that
COMMUTATOR
is for...)
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:
eqsel for = |
neqsel for <> |
scalarltsel for < |
scalarlesel for <= |
scalargtsel for > |
scalargesel for >= |
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
approximate-equality geometric operators use eqsel
on the assumption that
they'll usually only match a small fraction of the entries in a table.
You can use scalarltsel
, scalarlesel
,
scalargtsel
and scalargesel
for comparisons on
data types that have some sensible means of being converted into numeric
scalars for range comparisons. If possible, add the data type to those
understood by the function convert_to_scalar()
in
src/backend/utils/adt/selfuncs.c
.
(Eventually, this function should be replaced by per-data-type functions
identified through a column of the pg_type
system catalog; but that hasn't happened
yet.) If you do not do this, things will still work, but the optimizer's
estimates won't be as good as they could be.
Another useful built-in selectivity estimation function
is matchingsel
, which will work for almost any
binary operator, if standard MCV and/or histogram statistics are
collected for the input data type(s). Its default estimate is set to
twice the default estimate used in eqsel
, making
it most suitable for comparison operators that are somewhat less
strict than equality. (Or you could call the
underlying generic_restriction_selectivity
function, providing a different default estimate.)
There are additional selectivity estimation functions designed for geometric
operators in src/backend/utils/adt/geo_selfuncs.c
: areasel
, positionsel
,
and contsel
. At this writing these are just stubs, but you might want
to use them (or even better, improve them) anyway.
JOIN
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:
table1.column1 OP table2.column2
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.
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:
eqjoinsel for = |
neqjoinsel for <> |
scalarltjoinsel for < |
scalarlejoinsel for <= |
scalargtjoinsel for > |
scalargejoinsel for >= |
matchingjoinsel for generic matching operators |
areajoinsel for 2D area-based comparisons |
positionjoinsel for 2D position-based comparisons |
contjoinsel for 2D containment-based comparisons |
HASHES
The HASHES
clause, if present, tells the system that
it is permissible to use the hash join method for a join based on this
operator. HASHES
only makes sense for a binary operator that
returns boolean
, and in practice the operator must represent
equality for some data type or pair of data types.
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
some form of equality. In most cases it is only practical to support
hashing for operators that take the same data type on both sides.
However, sometimes it is possible to design compatible hash functions
for two or more data types; that is, functions that will generate the
same hash codes for “equal” values, even though the values
have different representations. For example, it's fairly simple
to arrange this property when hashing integers of different widths.
To be marked HASHES
, the join operator must appear
in a hash index operator family. This is not enforced when you create
the operator, since of course the referencing operator family couldn't
exist yet. But attempts to use the operator in hash joins will fail
at run time if no such operator family exists. The system needs the
operator family to find the data-type-specific hash function(s) for the
operator's input data type(s). Of course, you must also create suitable
hash functions before you can create the operator family.
Care should be exercised when preparing a hash function, because there
are machine-dependent ways in which it might fail to do the right thing.
For example, if your data type is a structure in which there might be
uninteresting pad bits, you cannot simply pass the whole structure to
hash_any
. (Unless you write your other operators and
functions to ensure that the unused bits are always zero, which is the
recommended strategy.)
Another example is that on machines that meet the IEEE
floating-point standard, negative zero and positive zero are different
values (different bit patterns) but they are defined to compare equal.
If a float value might contain negative zero then extra steps are needed
to ensure it generates the same hash value as positive zero.
A hash-joinable operator must have a commutator (itself if the two operand data types are the same, or a related equality operator if they are different) that appears in the same operator family. If this is not the case, planner errors might occur when the operator is used. Also, it is a good idea (but not strictly required) for a hash operator family that supports multiple data types to provide equality operators for every combination of the data types; this allows better optimization.
The function underlying a hash-joinable operator must be marked immutable or stable. If it is volatile, the system will never attempt to use the operator for a hash join.
If a hash-joinable operator has an underlying function that is marked
strict, the
function must also be complete: that is, it should return true or
false, never null, for any two nonnull inputs. If this rule is
not followed, hash-optimization of IN
operations might
generate wrong results. (Specifically, IN
might return
false where the correct answer according to the standard would be null;
or it might yield an error complaining that it wasn't prepared for a
null result.)
MERGES
The MERGES
clause, if present, tells the system that
it is permissible to use the merge-join method for a join based on this
operator. MERGES
only makes sense for a binary operator that
returns boolean
, and in practice the operator must represent
equality for some data type or pair of data types.
Merge join is based on the idea of sorting the left- and right-hand 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 it is possible to merge-join two
distinct data types so long as they are logically compatible. For
example, the smallint
-versus-integer
equality operator is merge-joinable.
We only need sorting operators that will bring both data types into a
logically compatible sequence.
To be marked MERGES
, the join operator must appear
as an equality member of a btree
index operator family.
This is not enforced when you create
the operator, since of course the referencing operator family couldn't
exist yet. But the operator will not actually be used for merge joins
unless a matching operator family can be found. The
MERGES
flag thus acts as a hint to the planner that
it's worth looking for a matching operator family.
A merge-joinable operator must have a commutator (itself if the two
operand data types are the same, or a related equality operator
if they are different) that appears in the same operator family.
If this is not the case, planner errors might occur when the operator
is used. Also, it is a good idea (but not strictly required) for
a btree
operator family that supports multiple data types to provide
equality operators for every combination of the data types; this
allows better optimization.
The function underlying a merge-joinable operator must be marked immutable or stable. If it is volatile, the system will never attempt to use the operator for a merge join.