For each combination of data types that a btree operator family provides comparison operators for, it must provide a comparison support function, registered in pg_amproc with support function number 1 and amproclefttype/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 in pg_amop). The comparison function must take two non-null values A and B and return an int32 value that is < 0, 0, or > 0 when A < B, A = B, or A > B, respectively. A null result is disallowed: all values of the data type must be comparable.

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

Optionally, a btree operator family may provide sort 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 in src/include/utils/sortsupport.h.

Optionally, a btree operator family may provide in_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 the RANGE offset PRECEDING and RANGE offset FOLLOWING frame bound types (see Section 4.2.8). Fundamentally, the extra information provided is how to add or subtract an offset value in a way that is compatible with the family's data ordering.

An in_range function must have the signature

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

val and base 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-in time_ops family provides an in_range function that has offset of type interval. A family can provide in_range functions for any of its supported types and one or more offset types. Each in_range function should be entered in pg_amproc with amproclefttype equal to type1 and amprocrighttype equal to type2.

The essential semantics of an in_range function depend on the two Boolean flag parameters. It should add or subtract base and offset, then compare val to the result, as follows:

Before doing so, the function should check the sign of offset: if it is less than zero, raise error ERRCODE_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 the in_range function so that the core code needn't understand what “less than zero” means for a particular data type.

An additional expectation is that in_range functions should, if practical, avoid throwing an error if base + offset or base - 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 that in_range's results agree with the normal sort order of the operator family.

The results of the in_range function must be consistent with the sort ordering imposed by the operator family. To be precise, given any fixed values of offset and sub, then:

Analogous statements with inverted conditions hold when less = false.

If the type being ordered (type1) is collatable, the appropriate collation OID will be passed to the in_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 provide equalimage (“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.

An equalimage function must have the signature

equalimage(opcintype oid) returns bool

The return value is static information about an operator class and collation. Returning true indicates that the order function for the operator class is guaranteed to only return 0 (“arguments are equal”) when its A and B arguments are also interchangeable without any loss of semantic information. Not registering an equalimage function or returning false indicates that this condition cannot be assumed to hold.

The opcintype argument is the pg_type.oid of the data type that the operator class indexes. This is a convenience that allows reuse of the same underlying equalimage function across operator classes. If opcintype is a collatable data type, the appropriate collation OID will be passed to the equalimage function, using the standard PG_GET_COLLATION() mechanism.

As far as the operator class is concerned, returning true indicates that deduplication is safe (or safe for the collation whose OID was passed to its equalimage function). However, the core code will only deem deduplication safe for an index when every indexed column uses an operator class that registers an equalimage function, and each function actually returns true when called.

Image equality is almost 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 of TOAST compression on input. Formally, when an operator class's equalimage function returns true, it is safe to assume that the datum_image_eq() C function will always agree with the operator class's order function (provided that the same collation OID is passed to both the equalimage and order 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-type equalimage 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 core PostgreSQL distribution is to register a stock, generic equalimage function. Most operator classes register btequalimage(), which indicates that deduplication is safe unconditionally. Operator classes for collatable data types such as text register btvarstrequalimage(), 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 provide options (“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.

An options support function must have the signature

options(relopts local_relopts *) returns void

The function is passed a pointer to a local_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 the PG_HAS_OPCLASS_OPTIONS() and PG_GET_OPCLASS_OPTIONS() macros.

Currently, no B-Tree operator class has an options 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 in PostgreSQL.