8.17. Range Types
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## 8.17. Range Types

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.

Every range type has a corresponding multirange type. A multirange is an ordered list of non-contiguous, non-empty, non-null ranges. Most range operators also work on multiranges, and they have a few functions of their own.

### 8.17.1. Built-in Range and Multirange Types

PostgreSQL comes with the following built-in range types:

- `int4range` — Range of `integer`, `int4multirange` — corresponding Multirange

- `int8range` — Range of `bigint`, `int8multirange` — corresponding Multirange

- `numrange` — Range of `numeric`, `nummultirange` — corresponding Multirange

- `tsrange` — Range of `timestamp without time zone`, `tsmultirange` — corresponding Multirange

- `tstzrange` — Range of `timestamp with time zone`, `tstzmultirange` — corresponding Multirange

- `daterange` — Range of `date`, `datemultirange` — corresponding Multirange

In addition, you can define your own range types; see CREATE TYPE for more information.

### 8.17.2. Examples

    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 9.54 and Table 9.56 for complete lists of operators and functions on range types.

### 8.17.3. Inclusive and Exclusive Bounds

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.

### 8.17.4. Infinite (Unbounded) Ranges

The lower bound of a range can be omitted, meaning that all values less than the upper bound are included in the range, e.g., `(,3]`. Likewise, if the upper bound of the range is omitted, then all values 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. Specifying a missing bound as inclusive is automatically converted to exclusive, e.g., `[,]` is converted to `(,)`. You can think of these missing values as +/-infinity, but they are special range type values and are considered to be beyond any range element type's +/-infinity values.

Element types that have the notion of “infinity” can use them as explicit bound values. For example, with timestamp ranges, `[today,infinity)` excludes the special `timestamp` value `infinity`, while `[today,infinity]` include it, as does `[today,)` and `[today,]`.

The functions `lower_inf` and `upper_inf` test for infinite lower and upper bounds of a range, respectively.

### 8.17.5. Range Input/Output

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.)

### Note

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;

The input for a multirange is curly brackets (`{` and `}`) containing zero or more valid ranges, separated by commas. Whitespace is permitted around the brackets and commas. This is intended to be reminiscent of array syntax, although multiranges are much simpler: they have just one dimension and there is no need to quote their contents. (The bounds of their ranges may be quoted as above however.)

Examples:

    SELECT '{}'::int4multirange;
    SELECT '{[3,7)}'::int4multirange;
    SELECT '{[3,7), [8,9)}'::int4multirange;

### 8.17.6. Constructing Ranges and Multiranges

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);

Each range type also has a multirange constructor with the same name as the multirange type. The constructor function takes zero or more arguments which are all ranges of the appropriate type. For example:

    SELECT nummultirange();
    SELECT nummultirange(numrange(1.0, 14.0));
    SELECT nummultirange(numrange(1.0, 14.0), numrange(20.0, 25.0));

### 8.17.7. Discrete Range Types

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.

### 8.17.8. Defining New Range Types

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.

When you define your own range you automatically get a corresponding multirange type.

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.

### 8.17.9. Indexing

GiST and SP-GiST indexes can be created for table columns of range types. GiST indexes can be also created for table columns of multirange types. For instance, to create a GiST index:

    CREATE INDEX reservation_idx ON reservation USING GIST (during);

A GiST or SP-GiST index on ranges can accelerate queries involving these range operators: `=`, `&&`, `<@`, `@>`, `<<`, `>>`, `-|-`, `&<`, and `&>`. A GiST index on multiranges can accelerate queries involving the same set of multirange operators. A GiST index on ranges and GiST index on multiranges can also accelerate queries involving these cross-type range to multirange and multirange to range operators correspondingly: `&&`, `<@`, `@>`, `<<`, `>>`, `-|-`, `&<`, and `&>`. See Table 9.54 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.

### 8.17.10. Constraints on Ranges

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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