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For each combination of data types that a btree operator family provides comparison operators for, it must provide a comparison support function, registered inpg_amproc with support function number 1 andamproclefttype/amprocrighttype equal to the left and right data types for the comparison (i.e., the same data types that the matching operators are registered with inpg_amop). The comparison function must take two non-null valuesA andB and return anint32 value that is<0,0, or>0 whenA<B,A=B, orA>B, respectively. A null result is disallowed: all values of the data type must be comparable. Seesrc/backend/access/nbtree/nbtcompare.c for examples.

If the compared values are of a collatable data type, the appropriate collation OID will be passed to the comparison support function, using the standardPG_GET_COLLATION() mechanism.

Optionally, a btree operator family may providesort support function(s), registered under support function number 2. These functions allow implementing comparisons for sorting purposes in a more efficient way than naively calling the comparison support function. The APIs involved in this are defined insrc/include/utils/sortsupport.h.

Optionally, a btree operator family may providein_range support function(s), registered under support function number 3. These are not used during btree index operations; rather, they extend the semantics of the operator family so that it can support window clauses containing theRANGEoffsetPRECEDING andRANGEoffsetFOLLOWING frame bound types (seeSection 4.2.8). Fundamentally, the extra information provided is how to add or subtract anoffset value in a way that is compatible with the family's data ordering.

Anin_range function must have the signature

in_range(val type1,base type1,offset type2,sub bool,less bool)returns bool

val andbase must be of the same type, which is one of the types supported by the operator family (i.e., a type for which it provides an ordering). However,offset could be of a different type, which might be one otherwise unsupported by the family. An example is that the built-intime_ops family provides anin_range function that hasoffset of typeinterval. A family can providein_range functions for any of its supported types and one or moreoffset types. Eachin_range function should be entered inpg_amproc withamproclefttype equal totype1 andamprocrighttype equal totype2.

The essential semantics of anin_range function depend on the two Boolean flag parameters. It should add or subtractbase andoffset, then compareval to the result, as follows:

Before doing so, the function should check the sign ofoffset: if it is less than zero, raise errorERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE (22013) with error text like“invalid preceding or following size in window function”. (This is required by the SQL standard, although nonstandard operator families might perhaps choose to ignore this restriction, since there seems to be little semantic necessity for it.) This requirement is delegated to thein_range function so that the core code needn't understand what“less than zero” means for a particular data type.

An additional expectation is thatin_range functions should, if practical, avoid throwing an error ifbase+offset orbase-offset would overflow. The correct comparison result can be determined even if that value would be out of the data type's range. Note that if the data type includes concepts such as“infinity” or“NaN”, extra care may be needed to ensure thatin_range's results agree with the normal sort order of the operator family.

The results of thein_range function must be consistent with the sort ordering imposed by the operator family. To be precise, given any fixed values ofoffset andsub, then:

Analogous statements with inverted conditions hold whenless = false.

If the type being ordered (type1) is collatable, the appropriate collation OID will be passed to thein_range function, using the standard PG_GET_COLLATION() mechanism.

in_range functions need not handle NULL inputs, and typically will be marked strict.

Optionally, a btree operator family may provideequalimage (“equality implies image equality”) support functions, registered under support function number 4. These functions allow the core code to determine when it is safe to apply the btree deduplication optimization. Currently,equalimage functions are only called when building or rebuilding an index.

Anequalimage function must have the signature

equalimage(opcintypeoid) returns bool

The return value is static information about an operator class and collation. Returningtrue indicates that theorder function for the operator class is guaranteed to only return0 (“arguments are equal”) when itsA andB arguments are also interchangeable without any loss of semantic information. Not registering anequalimage function or returningfalse indicates that this condition cannot be assumed to hold.

Theopcintype argument is thepg_type.oid of the data type that the operator class indexes. This is a convenience that allows reuse of the same underlyingequalimage function across operator classes. Ifopcintype is a collatable data type, the appropriate collation OID will be passed to theequalimage function, using the standardPG_GET_COLLATION() mechanism.

As far as the operator class is concerned, returningtrue indicates that deduplication is safe (or safe for the collation whose OID was passed to itsequalimage function). However, the core code will only deem deduplication safe for an index whenevery indexed column uses an operator class that registers anequalimage function, and each function actually returnstrue when called.

Image equality isalmost the same condition as simple bitwise equality. There is one subtle difference: When indexing a varlena data type, the on-disk representation of two image equal datums may not be bitwise equal due to inconsistent application ofTOAST compression on input. Formally, when an operator class'sequalimage function returnstrue, it is safe to assume that thedatum_image_eq() C function will always agree with the operator class'sorder function (provided that the same collation OID is passed to both theequalimage andorder functions).

The core code is fundamentally unable to deduce anything about the“equality implies image equality” status of an operator class within a multiple-data-type family based on details from other operator classes in the same family. Also, it is not sensible for an operator family to register a cross-typeequalimage function, and attempting to do so will result in an error. This is because“equality implies image equality” status does not just depend on sorting/equality semantics, which are more or less defined at the operator family level. In general, the semantics that one particular data type implements must be considered separately.

The convention followed by the operator classes included with the corePostgreSQL distribution is to register a stock, genericequalimage function. Most operator classes registerbtequalimage(), which indicates that deduplication is safe unconditionally. Operator classes for collatable data types such astext registerbtvarstrequalimage(), which indicates that deduplication is safe with deterministic collations. Best practice for third-party extensions is to register their own custom function to retain control.

Optionally, a B-tree operator family may provideoptions (“operator class specific options”) support functions, registered under support function number 5. These functions define a set of user-visible parameters that control operator class behavior.

Anoptions support function must have the signature

options(reloptslocal_relopts *) returns void

The function is passed a pointer to alocal_relopts struct, which needs to be filled with a set of operator class specific options. The options can be accessed from other support functions using thePG_HAS_OPCLASS_OPTIONS() andPG_GET_OPCLASS_OPTIONS() macros.

Currently, no B-Tree operator class has anoptions support function. B-tree doesn't allow flexible representation of keys like GiST, SP-GiST, GIN and BRIN do. So,options probably doesn't have much application in the current B-tree index access method. Nevertheless, this support function was added to B-tree for uniformity, and will probably find uses during further evolution of B-tree inPostgreSQL.