Range types are data types representing a range of values of
some element type (called the range's subtype). For instance, ranges of timestamp
might be used to represent the ranges of
time that a meeting room is reserved. In this case the data type is
tsrange
(short for “timestamp range”), and
timestamp
is the subtype. The subtype
must have a total order so that it is well-defined whether element
values are within, before, or after a range of values.
Range types are useful because they represent many element values in a single range value, and because concepts such as overlapping ranges can be expressed clearly. The use of time and date ranges for scheduling purposes is the clearest example; but price ranges, measurement ranges from an instrument, and so forth can also be useful.
PostgreSQL comes with the following built-in range types:
int4range
— Range of integer
int8range
— Range of bigint
numrange
— Range of numeric
tsrange
— Range of timestamp without time zone
tstzrange
— Range of timestamp with time zone
daterange
— Range of date
In addition, you can define your own range types; see CREATE TYPE for more information.
CREATE TABLE reservation (room int, during tsrange); INSERT INTO reservation VALUES (1108, '[2010-01-01 14:30, 2010-01-01 15:30)'); -- Containment SELECT int4range(10, 20) @> 3; -- Overlaps SELECT numrange(11.1, 22.2) && numrange(20.0, 30.0); -- Extract the upper bound SELECT upper(int8range(15, 25)); -- Compute the intersection SELECT int4range(10, 20) * int4range(15, 25); -- Is the range empty? SELECT isempty(numrange(1, 5));
See Table 9.50 and Table 9.51 for complete lists of operators and functions on range types.
Every non-empty range has two bounds, the lower bound and the upper bound. All points between these values are included in the range. An inclusive bound means that the boundary point itself is included in the range as well, while an exclusive bound means that the boundary point is not included in the range.
In the text form of a range, an inclusive lower bound is
represented by “[
” while an
exclusive lower bound is represented by “(
”. Likewise, an inclusive upper
bound is represented by “]
”, while an
exclusive upper bound is represented by “)
”. (See Section 8.17.5 for more
details.)
The functions lower_inc
and
upper_inc
test the inclusivity of the
lower and upper bounds of a range value, respectively.
The lower bound of a range can be omitted, meaning that all points less than the upper bound are included in the range. Likewise, if the upper bound of the range is omitted, then all points greater than the lower bound are included in the range. If both lower and upper bounds are omitted, all values of the element type are considered to be in the range.
This is equivalent to considering that the lower bound is “minus infinity”, or the upper bound is “plus infinity”, respectively. But note that these infinite values are never values of the range's element type, and can never be part of the range. (So there is no such thing as an inclusive infinite bound — if you try to write one, it will automatically be converted to an exclusive bound.)
Also, some element types have a notion of “infinity”, but that is
just another value so far as the range type mechanisms are
concerned. For example, in timestamp ranges, [today,]
means the same thing as [today,)
. But [today,infinity]
means something different from
[today,infinity)
— the latter excludes
the special timestamp
value infinity
.
The functions lower_inf
and
upper_inf
test for infinite lower and
upper bounds of a range, respectively.
The input for a range value must follow one of the following patterns:
(lower-bound
,upper-bound
) (lower-bound
,upper-bound
] [lower-bound
,upper-bound
) [lower-bound
,upper-bound
] empty
The parentheses or brackets indicate whether the lower and upper
bounds are exclusive or inclusive, as described previously. Notice
that the final pattern is empty
, which
represents an empty range (a range that contains no points).
The lower-bound
may be
either a string that is valid input for the subtype, or empty to
indicate no lower bound. Likewise, upper-bound
may be either a string
that is valid input for the subtype, or empty to indicate no upper
bound.
Each bound value can be quoted using "
(double quote) characters. This is necessary if
the bound value contains parentheses, brackets, commas, double
quotes, or backslashes, since these characters would otherwise be
taken as part of the range syntax. To put a double quote or
backslash in a quoted bound value, precede it with a backslash.
(Also, a pair of double quotes within a double-quoted bound value
is taken to represent a double quote character, analogously to the
rules for single quotes in SQL literal strings.) Alternatively, you
can avoid quoting and use backslash-escaping to protect all data
characters that would otherwise be taken as range syntax. Also, to
write a bound value that is an empty string, write ""
, since writing nothing means an infinite
bound.
Whitespace is allowed before and after the range value, but any whitespace between the parentheses or brackets is taken as part of the lower or upper bound value. (Depending on the element type, it might or might not be significant.)
These rules are very similar to those for writing field values in composite-type literals. See Section 8.16.6 for additional commentary.
Examples:
-- includes 3, does not include 7, and does include all points in between SELECT '[3,7)'::int4range; -- does not include either 3 or 7, but includes all points in between SELECT '(3,7)'::int4range; -- includes only the single point 4 SELECT '[4,4]'::int4range; -- includes no points (and will be normalized to 'empty') SELECT '[4,4)'::int4range;
Each range type has a constructor function with the same name as
the range type. Using the constructor function is frequently more
convenient than writing a range literal constant, since it avoids
the need for extra quoting of the bound values. The constructor
function accepts two or three arguments. The two-argument form
constructs a range in standard form (lower bound inclusive, upper
bound exclusive), while the three-argument form constructs a range
with bounds of the form specified by the third argument. The third
argument must be one of the strings “()
”, “(]
”, “[)
”, or “[]
”. For example:
-- The full form is: lower bound, upper bound, and text argument indicating -- inclusivity/exclusivity of bounds. SELECT numrange(1.0, 14.0, '(]'); -- If the third argument is omitted, '[)' is assumed. SELECT numrange(1.0, 14.0); -- Although '(]' is specified here, on display the value will be converted to -- canonical form, since int8range is a discrete range type (see below). SELECT int8range(1, 14, '(]'); -- Using NULL for either bound causes the range to be unbounded on that side. SELECT numrange(NULL, 2.2);
A discrete range is one whose element type has a well-defined
“step”, such
as integer
or date
. In these types two elements can be said to be
adjacent, when there are no valid values between them. This
contrasts with continuous ranges, where it's always (or almost
always) possible to identify other element values between two given
values. For example, a range over the numeric
type is continuous, as is a range over
timestamp
. (Even though timestamp
has limited precision, and so could
theoretically be treated as discrete, it's better to consider it
continuous since the step size is normally not of interest.)
Another way to think about a discrete range type is that there
is a clear idea of a “next” or “previous” value for each element value.
Knowing that, it is possible to convert between inclusive and
exclusive representations of a range's bounds, by choosing the next
or previous element value instead of the one originally given. For
example, in an integer range type [4,8]
and (3,9)
denote the same set of values; but this would not be so for a range
over numeric.
A discrete range type should have a canonicalization function that is aware of the desired step size for the element type. The canonicalization function is charged with converting equivalent values of the range type to have identical representations, in particular consistently inclusive or exclusive bounds. If a canonicalization function is not specified, then ranges with different formatting will always be treated as unequal, even though they might represent the same set of values in reality.
The built-in range types int4range
,
int8range
, and daterange
all use a canonical form that includes the
lower bound and excludes the upper bound; that is, [)
. User-defined range types can use other
conventions, however.
Users can define their own range types. The most common reason
to do this is to use ranges over subtypes not provided among the
built-in range types. For example, to define a new range type of
subtype float8
:
CREATE TYPE floatrange AS RANGE ( subtype = float8, subtype_diff = float8mi ); SELECT '[1.234, 5.678]'::floatrange;
Because float8
has no meaningful
“step”, we do
not define a canonicalization function in this example.
Defining your own range type also allows you to specify a different subtype B-tree operator class or collation to use, so as to change the sort ordering that determines which values fall into a given range.
If the subtype is considered to have discrete rather than
continuous values, the CREATE TYPE
command should specify a canonical
function. The canonicalization function takes an input range value,
and must return an equivalent range value that may have different
bounds and formatting. The canonical output for two ranges that
represent the same set of values, for example the integer ranges
[1, 7]
and [1,
8)
, must be identical. It doesn't matter which
representation you choose to be the canonical one, so long as two
equivalent values with different formattings are always mapped to
the same value with the same formatting. In addition to adjusting
the inclusive/exclusive bounds format, a canonicalization function
might round off boundary values, in case the desired step size is
larger than what the subtype is capable of storing. For instance, a
range type over timestamp
could be
defined to have a step size of an hour, in which case the
canonicalization function would need to round off bounds that
weren't a multiple of an hour, or perhaps throw an error
instead.
In addition, any range type that is meant to be used with GiST
or SP-GiST indexes should define a subtype difference, or
subtype_diff
, function. (The index
will still work without subtype_diff
,
but it is likely to be considerably less efficient than if a
difference function is provided.) The subtype difference function
takes two input values of the subtype, and returns their difference
(i.e., X
minus Y
) represented as a float8
value. In our example above, the function
float8mi
that underlies the regular
float8
minus operator can be used; but
for any other subtype, some type conversion would be necessary.
Some creative thought about how to represent differences as numbers
might be needed, too. To the greatest extent possible, the
subtype_diff
function should agree
with the sort ordering implied by the selected operator class and
collation; that is, its result should be positive whenever its
first argument is greater than its second according to the sort
ordering.
A less-oversimplified example of a subtype_diff
function is:
CREATE FUNCTION time_subtype_diff(x time, y time) RETURNS float8 AS 'SELECT EXTRACT(EPOCH FROM (x - y))' LANGUAGE sql STRICT IMMUTABLE; CREATE TYPE timerange AS RANGE ( subtype = time, subtype_diff = time_subtype_diff ); SELECT '[11:10, 23:00]'::timerange;
See CREATE TYPE for more information about creating range types.
GiST and SP-GiST indexes can be created for table columns of range types. For instance, to create a GiST index:
CREATE INDEX reservation_idx ON reservation USING GIST (during);
A GiST or SP-GiST index can accelerate queries involving these
range operators: =
, &&
, <@
,
@>
, <<
, >>
,
-|-
, &<
, and &>
(see Table 9.50 for
more information).
In addition, B-tree and hash indexes can be created for table
columns of range types. For these index types, basically the only
useful range operation is equality. There is a B-tree sort ordering
defined for range values, with corresponding <
and >
operators, but the ordering is rather arbitrary and not usually
useful in the real world. Range types' B-tree and hash support is
primarily meant to allow sorting and hashing internally in queries,
rather than creation of actual indexes.
While UNIQUE
is a natural
constraint for scalar values, it is usually unsuitable for range
types. Instead, an exclusion constraint is often more appropriate
(see CREATE TABLE ...
CONSTRAINT ... EXCLUDE). Exclusion constraints allow the
specification of constraints such as “non-overlapping” on a
range type. For example:
CREATE TABLE reservation ( during tsrange, EXCLUDE USING GIST (during WITH &&) );
That constraint will prevent any overlapping values from existing in the table at the same time:
INSERT INTO reservation VALUES ('[2010-01-01 11:30, 2010-01-01 15:00)'); INSERT 0 1 INSERT INTO reservation VALUES ('[2010-01-01 14:45, 2010-01-01 15:45)'); ERROR: conflicting key value violates exclusion constraint "reservation_during_excl" DETAIL: Key (during)=(["2010-01-01 14:45:00","2010-01-01 15:45:00")) conflicts with existing key (during)=(["2010-01-01 11:30:00","2010-01-01 15:00:00")).
You can use the btree_gist
extension to define exclusion constraints on plain scalar data
types, which can then be combined with range exclusions for maximum
flexibility. For example, after btree_gist
is installed, the following constraint
will reject overlapping ranges only if the meeting room numbers are
equal:
CREATE EXTENSION btree_gist; CREATE TABLE room_reservation ( room text, during tsrange, EXCLUDE USING GIST (room WITH =, during WITH &&) ); INSERT INTO room_reservation VALUES ('123A', '[2010-01-01 14:00, 2010-01-01 15:00)'); INSERT 0 1 INSERT INTO room_reservation VALUES ('123A', '[2010-01-01 14:30, 2010-01-01 15:30)'); ERROR: conflicting key value violates exclusion constraint "room_reservation_room_during_excl" DETAIL: Key (room, during)=(123A, ["2010-01-01 14:30:00","2010-01-01 15:30:00")) conflicts with existing key (room, during)=(123A, ["2010-01-01 14:00:00","2010-01-01 15:00:00")). INSERT INTO room_reservation VALUES ('123B', '[2010-01-01 14:30, 2010-01-01 15:30)'); INSERT 0 1
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