As shown in Table 37.8, btree defines one required and two optional support functions.

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. See src/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 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.