8.1. Numeric Types
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## 8.1. Numeric Types #

Numeric types consist of two-, four-, and eight-byte integers, four- and eight-byte floating-point numbers, and selectable-precision decimals. Table 8.2 lists the available types.

Table 8.2. Numeric Types

Name | Storage Size | Description | Range
--- | --- | --- | ---
`smallint` | 2 bytes | small-range integer | -32768 to +32767
`integer` | 4 bytes | typical choice for integer | -2147483648 to +2147483647
`bigint` | 8 bytes | large-range integer | -9223372036854775808 to +9223372036854775807
`decimal` | variable | user-specified precision, exact | up to 131072 digits before the decimal point; up to 16383 digits after the decimal point
`numeric` | variable | user-specified precision, exact | up to 131072 digits before the decimal point; up to 16383 digits after the decimal point
`real` | 4 bytes | variable-precision, inexact | 6 decimal digits precision
`double precision` | 8 bytes | variable-precision, inexact | 15 decimal digits precision
`smallserial` | 2 bytes | small autoincrementing integer | 1 to 32767
`serial` | 4 bytes | autoincrementing integer | 1 to 2147483647
`bigserial` | 8 bytes | large autoincrementing integer | 1 to 9223372036854775807

The syntax of constants for the numeric types is described in Section 4.1.2. The numeric types have a full set of corresponding arithmetic operators and functions. Refer to Chapter 9 for more information. The following sections describe the types in detail.

### 8.1.1. Integer Types #

The types `smallint`, `integer`, and `bigint` store whole numbers, that is, numbers without fractional components, of various ranges. Attempts to store values outside of the allowed range will result in an error.

The type `integer` is the common choice, as it offers the best balance between range, storage size, and performance. The `smallint` type is generally only used if disk space is at a premium. The `bigint` type is designed to be used when the range of the `integer` type is insufficient.

SQL only specifies the integer types `integer` (or `int`), `smallint`, and `bigint`. The type names `int2`, `int4`, and `int8` are extensions, which are also used by some other SQL database systems.

### 8.1.2. Arbitrary Precision Numbers #

The type `numeric` can store numbers with a very large number of digits. It is especially recommended for storing monetary amounts and other quantities where exactness is required. Calculations with `numeric` values yield exact results where possible, e.g., addition, subtraction, multiplication. However, calculations on `numeric` values are very slow compared to the integer types, or to the floating-point types described in the next section.

We use the following terms below: The precision of a `numeric` is the total count of significant digits in the whole number, that is, the number of digits to both sides of the decimal point. The scale of a `numeric` is the count of decimal digits in the fractional part, to the right of the decimal point. So the number 23.5141 has a precision of 6 and a scale of 4. Integers can be considered to have a scale of zero.

Both the maximum precision and the maximum scale of a `numeric` column can be configured. To declare a column of type `numeric` use the syntax:

    NUMERIC(precision, scale)

The precision must be positive, while the scale may be positive or negative (see below). Alternatively:

    NUMERIC(precision)

selects a scale of 0. Specifying:

    NUMERIC

without any precision or scale creates an “unconstrained numeric” column in which numeric values of any length can be stored, up to the implementation limits. A column of this kind will not coerce input values to any particular scale, whereas `numeric` columns with a declared scale will coerce input values to that scale. (The SQL standard requires a default scale of 0, i.e., coercion to integer precision. We find this a bit useless. If you're concerned about portability, always specify the precision and scale explicitly.)

### Note

The maximum precision that can be explicitly specified in a `numeric` type declaration is 1000. An unconstrained `numeric` column is subject to the limits described in Table 8.2.

If the scale of a value to be stored is greater than the declared scale of the column, the system will round the value to the specified number of fractional digits. Then, if the number of digits to the left of the decimal point exceeds the declared precision minus the declared scale, an error is raised. For example, a column declared as

    NUMERIC(3, 1)

will round values to 1 decimal place and can store values between -99.9 and 99.9, inclusive.

Beginning in PostgreSQL 15, it is allowed to declare a `numeric` column with a negative scale. Then values will be rounded to the left of the decimal point. The precision still represents the maximum number of non-rounded digits. Thus, a column declared as

    NUMERIC(2, -3)

will round values to the nearest thousand and can store values between -99000 and 99000, inclusive. It is also allowed to declare a scale larger than the declared precision. Such a column can only hold fractional values, and it requires the number of zero digits just to the right of the decimal point to be at least the declared scale minus the declared precision. For example, a column declared as

    NUMERIC(3, 5)

will round values to 5 decimal places and can store values between -0.00999 and 0.00999, inclusive.

### Note

PostgreSQL permits the scale in a `numeric` type declaration to be any value in the range -1000 to 1000. However, the SQL standard requires the scale to be in the range 0 to `precision`. Using scales outside that range may not be portable to other database systems.

Numeric values are physically stored without any extra leading or trailing zeroes. Thus, the declared precision and scale of a column are maximums, not fixed allocations. (In this sense the `numeric` type is more akin to `varchar(`n`)` than to `char(`n`)`.) The actual storage requirement is two bytes for each group of four decimal digits, plus three to eight bytes overhead.

In addition to ordinary numeric values, the `numeric` type has several special values:

`Infinity`
`-Infinity`
`NaN`

These are adapted from the IEEE 754 standard, and represent “infinity”, “negative infinity”, and “not-a-number”, respectively. When writing these values as constants in an SQL command, you must put quotes around them, for example `UPDATE table SET x = '-Infinity'`. On input, these strings are recognized in a case-insensitive manner. The infinity values can alternatively be spelled `inf` and `-inf`.

The infinity values behave as per mathematical expectations. For example, `Infinity` plus any finite value equals `Infinity`, as does `Infinity` plus `Infinity`; but `Infinity` minus `Infinity` yields `NaN` (not a number), because it has no well-defined interpretation. Note that an infinity can only be stored in an unconstrained `numeric` column, because it notionally exceeds any finite precision limit.

The `NaN` (not a number) value is used to represent undefined calculational results. In general, any operation with a `NaN` input yields another `NaN`. The only exception is when the operation's other inputs are such that the same output would be obtained if the `NaN` were to be replaced by any finite or infinite numeric value; then, that output value is used for `NaN` too. (An example of this principle is that `NaN` raised to the zero power yields one.)

### Note

In most implementations of the “not-a-number” concept, `NaN` is not considered equal to any other numeric value (including `NaN`). In order to allow `numeric` values to be sorted and used in tree-based indexes, PostgreSQL treats `NaN` values as equal, and greater than all non-`NaN` values.

The types `decimal` and `numeric` are equivalent. Both types are part of the SQL standard.

When rounding values, the `numeric` type rounds ties away from zero, while (on most machines) the `real` and `double precision` types round ties to the nearest even number. For example:

    SELECT x,
      round(x::numeric) AS num_round,
      round(x::double precision) AS dbl_round
    FROM generate_series(-3.5, 3.5, 1) as x;
      x   | num_round | dbl_round
    ------+-----------+-----------
     -3.5 |        -4 |        -4
     -2.5 |        -3 |        -2
     -1.5 |        -2 |        -2
     -0.5 |        -1 |        -0
      0.5 |         1 |         0
      1.5 |         2 |         2
      2.5 |         3 |         2
      3.5 |         4 |         4
    (8 rows)

### 8.1.3. Floating-Point Types #

The data types `real` and `double precision` are inexact, variable-precision numeric types. On all currently supported platforms, these types are implementations of IEEE Standard 754 for Binary Floating-Point Arithmetic (single and double precision, respectively), to the extent that the underlying processor, operating system, and compiler support it.

Inexact means that some values cannot be converted exactly to the internal format and are stored as approximations, so that storing and retrieving a value might show slight discrepancies. Managing these errors and how they propagate through calculations is the subject of an entire branch of mathematics and computer science and will not be discussed here, except for the following points:

- If you require exact storage and calculations (such as for monetary amounts), use the `numeric` type instead.

- If you want to do complicated calculations with these types for anything important, especially if you rely on certain behavior in boundary cases (infinity, underflow), you should evaluate the implementation carefully.

- Comparing two floating-point values for equality might not always work as expected.

On all currently supported platforms, the `real` type has a range of around 1E-37 to 1E+37 with a precision of at least 6 decimal digits. The `double precision` type has a range of around 1E-307 to 1E+308 with a precision of at least 15 digits. Values that are too large or too small will cause an error. Rounding might take place if the precision of an input number is too high. Numbers too close to zero that are not representable as distinct from zero will cause an underflow error.

By default, floating point values are output in text form in their shortest precise decimal representation; the decimal value produced is closer to the true stored binary value than to any other value representable in the same binary precision. (However, the output value is currently never exactly midway between two representable values, in order to avoid a widespread bug where input routines do not properly respect the round-to-nearest-even rule.) This value will use at most 17 significant decimal digits for `float8` values, and at most 9 digits for `float4` values.

### Note

This shortest-precise output format is much faster to generate than the historical rounded format.

For compatibility with output generated by older versions of PostgreSQL, and to allow the output precision to be reduced, the extra_float_digits parameter can be used to select rounded decimal output instead. Setting a value of 0 restores the previous default of rounding the value to 6 (for `float4`) or 15 (for `float8`) significant decimal digits. Setting a negative value reduces the number of digits further; for example -2 would round output to 4 or 13 digits respectively.

Any value of extra_float_digits greater than 0 selects the shortest-precise format.

### Note

Applications that wanted precise values have historically had to set extra_float_digits to 3 to obtain them. For maximum compatibility between versions, they should continue to do so.

In addition to ordinary numeric values, the floating-point types have several special values:

`Infinity`
`-Infinity`
`NaN`

These represent the IEEE 754 special values “infinity”, “negative infinity”, and “not-a-number”, respectively. When writing these values as constants in an SQL command, you must put quotes around them, for example `UPDATE table SET x = '-Infinity'`. On input, these strings are recognized in a case-insensitive manner. The infinity values can alternatively be spelled `inf` and `-inf`.

### Note

IEEE 754 specifies that `NaN` should not compare equal to any other floating-point value (including `NaN`). In order to allow floating-point values to be sorted and used in tree-based indexes, PostgreSQL treats `NaN` values as equal, and greater than all non-`NaN` values.

PostgreSQL also supports the SQL-standard notations `float` and `float(`p`)` for specifying inexact numeric types. Here, `p` specifies the minimum acceptable precision in binary digits. PostgreSQL accepts `float(1)` to `float(24)` as selecting the `real` type, while `float(25)` to `float(53)` select `double precision`. Values of `p` outside the allowed range draw an error. `float` with no precision specified is taken to mean `double precision`.

### 8.1.4. Serial Types #

### Note

This section describes a PostgreSQL-specific way to create an autoincrementing column. Another way is to use the SQL-standard identity column feature, described at CREATE TABLE.

The data types `smallserial`, `serial` and `bigserial` are not true types, but merely a notational convenience for creating unique identifier columns (similar to the `AUTO_INCREMENT` property supported by some other databases). In the current implementation, specifying:

    CREATE TABLE tablename (
        colname SERIAL
    );

is equivalent to specifying:

    CREATE SEQUENCE tablename_colname_seq AS integer;
    CREATE TABLE tablename (
        colname integer NOT NULL DEFAULT nextval('tablename_colname_seq')
    );
    ALTER SEQUENCE tablename_colname_seq OWNED BY tablename.colname;

Thus, we have created an integer column and arranged for its default values to be assigned from a sequence generator. A `NOT NULL` constraint is applied to ensure that a null value cannot be inserted. (In most cases you would also want to attach a `UNIQUE` or `PRIMARY KEY` constraint to prevent duplicate values from being inserted by accident, but this is not automatic.) Lastly, the sequence is marked as “owned by” the column, so that it will be dropped if the column or table is dropped.

### Note

Because `smallserial`, `serial` and `bigserial` are implemented using sequences, there may be "holes" or gaps in the sequence of values which appears in the column, even if no rows are ever deleted. A value allocated from the sequence is still "used up" even if a row containing that value is never successfully inserted into the table column. This may happen, for example, if the inserting transaction rolls back. See `nextval()` in Section 9.17 for details.

To insert the next value of the sequence into the `serial` column, specify that the `serial` column should be assigned its default value. This can be done either by excluding the column from the list of columns in the `INSERT` statement, or through the use of the `DEFAULT` key word.

The type names `serial` and `serial4` are equivalent: both create `integer` columns. The type names `bigserial` and `serial8` work the same way, except that they create a `bigint` column. `bigserial` should be used if you anticipate the use of more than 231 identifiers over the lifetime of the table. The type names `smallserial` and `serial2` also work the same way, except that they create a `smallint` column.

The sequence created for a `serial` column is automatically dropped when the owning column is dropped. You can drop the sequence without dropping the column, but this will force removal of the column default expression.

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