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## 63.3. B-Tree Support Functions

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

*and return an*

`B`

`int32`

value that
is `<`

`0`

, `0`

,
or `>`

`0`

when

`A`

`<`

*,*

`B`

`A`

`=`

*, or*

`B`

`A`

`>`

*, respectively. A null result is disallowed: all values of the data type must be comparable. See*

`B`

`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(type1,`val`

type1,`base`

type2,`offset`

bool,`sub`

bool) returns bool`less`

* val* and

*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,*

`base`

*could be of a different type, which might be one otherwise unsupported by the family. An example is that the built-in*

`offset`

`time_ops`

family provides
an `in_range`

function that
has *of type*

`offset`

`interval`

.
A family can provide `in_range`

functions for any of
its supported types and one or more *types. Each*

`offset`

`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

*, then compare*

`offset`

*to the result, as follows:*

`val`

if

`!`

and`sub`

`!`

, return`less`

`val`

`>=`

(`base`

`+`

)`offset`

if

`!`

and`sub`

, return`less`

`val`

`<=`

(`base`

`+`

)`offset`

if

and`sub`

`!`

, return`less`

`val`

`>=`

(`base`

`-`

)`offset`

if

and`sub`

, return`less`

`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`

`-`

*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*

`offset`

`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

*, then:*

`sub`

If

`in_range`

with= true is true for some`less`

and`val1`

, it must be true for every`base`

`val2`

`<=`

with the same`val1`

.`base`

If

`in_range`

with= true is false for some`less`

and`val1`

, it must be false for every`base`

`val2`

`>=`

with the same`val1`

.`base`

If

`in_range`

with= true is true for some`less`

and`val`

, it must be true for every`base1`

`base2`

`>=`

with the same`base1`

.`val`

If

`in_range`

with= true is false for some`less`

and`val`

, it must be false for every`base1`

`base2`

`<=`

with the same`base1`

.`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.