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(valtype1,basetype1,offsettype2,subbool,lessbool) 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.