## 64.3. B-Tree Support Functions

As shown in Table 38.8, 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:

- if `!``sub` and `!``less`, return `val` `>=` (`base` `+` `offset`)

- if `!``sub` and `less`, return `val` `<=` (`base` `+` `offset`)

- if `sub` and `!``less`, return `val` `>=` (`base` `-` `offset`)

- if `sub` and `less`, return `val` `<=` (`base` `-` `offset`)

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:

- If `in_range` with `less` = true is true for some `val1` and `base`, it must be true for every `val2` `<=` `val1` with the same `base`.

- If `in_range` with `less` = true is false for some `val1` and `base`, it must be false for every `val2` `>=` `val1` with the same `base`.

- If `in_range` with `less` = true is true for some `val` and `base1`, it must be true for every `base2` `>=` `base1` with the same `val`.

- If `in_range` with `less` = true is false for some `val` and `base1`, it must be false for every `base2` `<=` `base1` with the same `val`.

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.