This talk explores the theory behind operator classes and families, including the assumptions data type-independent code is and is not entitled to make based on available operator classes. We will walk through the creation of new operator classes, some practical and others deliberately perverse, and examine some exceptional operator classes already present in PostgreSQL.

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I know greater-than-or-equal-to when I see it!
Noah Misch | 2014-05-22
>= <>&&
<@

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■ Index access methods (pg_am)
− Type-independent; specific to certain index layout
− btree, hash, gist, gin, spgist
■ Operator classes (pg_opclass)
− Specific to a data type + index access method
− Tightly related: operator families (pg_opfamily)
− int4_ops, text_ops
Layers of Index Support

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■ In general: ties a data type to an access method
■ The case of btree: comparison function and operators
What is an operator class?
CREATE TABLE t (c date PRIMARY KEY);
INSERT INTO t VALUES ('2014-01-01');
INSERT INTO t VALUES ('2015-01-01');
...
-- <(date,date) operator
SELECT * FROM t WHERE c < current_date;

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■ Extends operator support to multiple data types
■ Relevant for btree and hash only
What is an operator family?
CREATE TABLE t (c date PRIMARY KEY);
INSERT INTO t VALUES ('2014-01-01');
INSERT INTO t VALUES ('2015-01-01');
...
-- <(date,timestamptz) operator
SELECT * FROM t WHERE c < now();

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■ FUNCTION entries maintain the index
■ List of OPERATOR qualified to exploit the index
■ “equal-sign operator” vs. “equality operator”
btree int4_ops walk-through
CREATE OPERATOR FAMILY integer_ops USING btree;
CREATE OPERATOR CLASS int4_ops
DEFAULT FOR TYPE integer
USING btree FAMILY integer_ops AS
FUNCTION 1 btint4cmp(integer, integer),
OPERATOR 1 <,
OPERATOR 2 <=,
OPERATOR 3 =,
OPERATOR 4 >=,
OPERATOR 5 >;

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System Catalog Representation
pg_am
btree
pg_opclass
int4_ops
pg_opfamily
integer_ops
pg_opclass
int2_ops
pg_amproc
btint4cmp
pg_amproc
btint24cmp
pg_amproc
btint2cmp
pg_amop
<(int4,int4)
pg_amop
<(int2,int4)
pg_amop
<(int2,int2)

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■ btree: other sort orders
− text_pattern_ops
■ hash: not done in practice
■ gin, gist, spgist:
fruitful opportunities
Multiple Operator Classes

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ORDER BY
-- uses btree text_ops
ORDER BY textcol;
-- uses btree text_pattern_ops
ORDER BY textcol USING ~<~;
-- can use e.g. gist_trgm_ops
ORDER BY textcol <-> 'search condition';

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■ UNION
■ GROUP BY, DISTINCT
■ array, composite type comparisons
■ Choice of default equality semantics is important
Equality
[local] test=# SELECT DISTINCT x
FROM unnest(array[1.00, 1.1, 1.0]) t(x);
x
──────
1.1
1.00
(2 rows)

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■ Operator names like “=” and “<” are not special ...
■ … excepting CASE, IN, IS DISTINCT FROM, etc
Equality Surprises
[local] test=# SELECT DISTINCT x
FROM unnest(array['(1,1),(0,0)',
'(2,2),(1,1)']::box[]) t(x);
ERROR: could not identify an equality
operator for type box
[local] test=# SELECT '(1,1),(0,0)'::box IN
('(2,2),(1,1)'::box);
?column?
──────────
t

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Merge Join
[local] test=# SET enable_hashjoin = off;
SET
[local] test=# EXPLAIN (costs off)
SELECT opfmethod, opfname, array_agg(amopopr)
FROM pg_amop ao JOIN pg_opfamily f
ON amopfamily = f.oid GROUP BY 1,2;
QUERY PLAN
─────────────────────────────────────────────
HashAggregate
Group Key: f.opfmethod, f.opfname
-> Merge Join
Merge Cond: (f.oid = ao.amopfamily)
-> Sort
Sort Key: f.oid
-> Seq Scan on pg_opfamily f
-> Sort
Sort Key: ao.amopfamily
-> Seq Scan on pg_amop ao

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Hash Join
[local] test=# EXPLAIN (costs off)
SELECT opfmethod, opfname, array_agg(amopopr)
FROM pg_amop ao JOIN pg_opfamily f
ON amopfamily = f.oid GROUP BY 1,2;
QUERY PLAN
─────────────────────────────────────────────
HashAggregate
Group Key: f.opfmethod, f.opfname
-> Hash Join
Hash Cond: (ao.amopfamily = f.oid)
-> Seq Scan on pg_amop ao
-> Hash
-> Seq Scan on pg_opfamily f

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■ Don't hard-code “=”
■ Which equality semantics?
− btree/hash default equality
− exact match (output comparison; record_image_ops)
■ Do look up equality by operator class
− backend: TYPECACHE_EQ_OPR
− frontend: copy its algorithm
■ Not all types have these operations
Writing Generic Data Type Consumers

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■ Choice of default equality semantics is important
− Option to omit them entirely (xml, json, box)
■ Try to include a default btree operator class
■ Default hash operator class is then easy
■ Other access methods are situation-specific
− gin for container-like types
− gist often starts with the search strategy, not the type
Implementing Data Types

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Questions?

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■ http://www.postgresql.org/docs/current/static/xindex.html
■ contrib/btree_gist, contrib/btree_gin
■ Other built-in and contrib operator classes
■ ATAddForeignKeyConstraint()
Further Reading

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hash int4_ops
CREATE OPERATOR CLASS int4_ops
DEFAULT FOR TYPE integer
USING hash FAMILY integer_ops AS
FUNCTION 1 hashint4(integer),
OPERATOR 1 =;

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Array Element Searches: gin _int4_ops
CREATE OPERATOR CLASS _int4_ops
DEFAULT FOR TYPE integer[]
USING gin FAMILY array_ops AS
STORAGE integer,
FUNCTION 1 btint4cmp(integer,integer),
FUNCTION 2 ginarrayextract(...),
FUNCTION 3 ginqueryarrayextract(...),
FUNCTION 4 ginarrayconsistent(...),
OPERATOR 1 &&(anyarray,anyarray),
OPERATOR 2 @>(anyarray,anyarray),
OPERATOR 3 <@(anyarray,anyarray),
OPERATOR 4 =(anyarray,anyarray);