# 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.

## Built-in Range Types

Greenplum Database 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

## 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 Range Functions and Operators for complete lists of operators and functions on range types.

## 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 Range Functions and Operators for more details.)

The functions lower_inc and upper_inc test the inclusivity of the lower and upper bounds of a range value, respectively.

## Infinite (Unbounded) Ranges

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.

## 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.)

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;
```

## Constructing Ranges

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);
```

## 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.

## 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.

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;
```

```CREATE INDEX reservation_idx ON reservation USING GIST (during);